Supplementary Information

library(dplyr)

library(ggplot2)
library(ggforce)
library(ggpubr)
library(cowplot)
library(gridExtra)
library(colorspace)

library(gamlss)

library(kableExtra)

library(rsq)

fCO2.atm.2020 <- 411.51 * 1e-6 # oct 2020
fCO2.atm.2019 <- 408.75 * 1e-6 # oct 2019
fCO2.atm.2004 <- 374.63 * 1e-6 # oct 2004
fCO2.atm.1995 <- 360.17 * 1e-6

library(captioner)
fig_nums <- captioner() 
tab_nums <- captioner(prefix = "Table")

1 Bookdown documentation

https://bookdown.org/yihui/bookdown/a-single-document.html

2 Import data

norway <- readRDS("norway.rds")
nlss <- readRDS("nlss.rds")

norway$TOC_mg <- norway$TOC*12.011*1e3
norway$TOC_umol <- norway$TOC*1e6
norway$TA_ueq <- norway$TA * 1e6
norway$CA_ueq <- norway$CA * 1e6
norway$DIC_mg <- norway$DIC*12.011*1e3
norway$DIC_umol <- norway$DIC * 1e6
norway$CA_ueq <- norway$CA * 1e6
norway$Hplus_umol <- norway$Hplus *1e6
norway$invHplus_umol <- 1/norway$Hplus *1e6
norway$invHplus <- 1/norway$Hplus

nlss <- readRDS("nlss.rds")
nlss$invHplus <- 1/nlss$Hplus
nlss$TOC_mg <- nlss$TOC*12.011*1e3

ggplot(nlss)+geom_point(aes(x=long, y = lat, col = TOC))+
  borders(regions = c("Norway","Sweden","Finland"))+ylim(55,72)+xlim(4,32)+
  scale_fill_continuous_divergingx(palette = "RdYlBu", aesthetics = c("fill","col"), mid = 0.001, rev = T)+ 
  theme_minimal()

Figure 1: Map of TOC in mg/L in the Northern Lake Survey

3 Estimation of organic and carbonate alkalinity

3.1 Carbonate speciation N112 / CBA

The concentration of the carbonate species in the N112 and CBA survey is calculated directly from the measured partial pressure of \(CO_2\) (Appelo and Postma 2005):

\(pCO_2 = [H_2CO_3]/K_0\)

\([HCO3^-] = K_1 \times [H_2CO_3]/[H^+]\)

\([CO_3^{2-}] = K_2 \times [HCO_3 ^- ] / [H ^+]\)

\([TIC] = [H_2CO_3] + [HCO_3^-]+[CO_3 ^{2-}]\)

\(K_0\) is Henry’s constant from Weiss (1974). \(K_1\) and \(K_2\) are ionization constants of \(H_2CO_3\) and \(HCO_3^-\) , respectively obtained from Herbert S. Harned and Davis (1943) and Herbert S. Harned and Scholes (1941) and are adjusted for temperature.

In freshwater samples, the chemical activity of carbonate species is assumed to be equal to the molar concentration. Therefore, molar concentration is used in all equilibrium equations.

Liu, Butman, and Raymond (2020) reported that in water with low ionic strength, the pH is underestimated by 0.1 to 0.5 units.  We chose to not correct pH in this study because the ionic strength was not available for the N112 survey. Since only one lake in the Northern Lakes Survey had a pH inferior to 5, we assumed that the measurement errors would be minimal.

ggplot(norway, aes(x = pH))+
  geom_point(aes(y = H2CO3, col = "H2CO3"), alpha = 0.5)+
  geom_point(aes(y = HCO3, col = "HCO3"), alpha = 0.5)+
  geom_point(aes(y = CO3, col = "CO3"), alpha = 0.5)+
  labs(y = "Carbonate species (mol/L)", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3","orange"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

Figure 2: Concentration of carbonate species in mol/L in the CBA and N112 surveys

ggplot(norway,aes(x= pH))+geom_point(aes(y = ta_fCO2, col = "pCO2 from TA"), alpha = 0.5)+
  geom_point(aes(y = fCO2, col = "Measured pCO2"), alpha = 0.5)+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_bw(base_size = 15)+
  theme(legend.position = "bottom")

Figure 3: Measured (red) and calculated (blue) pCO2 in atm for the CBA and N112 surveys

toc_boxplot <- ggplot(norway)+
  geom_boxplot(aes(x = "TOC", y = TOC, col = survey))+
  geom_boxplot(aes(x = "DIC", y = DIC, col = survey))+
  labs(x = "", y = "concentration, mol/L")+
  scale_color_manual(values = c("firebrick", "dodgerblue"))+
  theme_minimal()+
  theme(legend.position = "bottom")

toc_boxplot

Figure 4: Boxplot of DIC and TOC in mol/L for the CBA survey (red) and N112 survey (blue)

3.2 Organic alkalinity as OA = TA - CA

Method also used in Couturier et al. (2022).

norway$OA <- with(norway, TA-CA)

ggarrange(
ggplot(norway)+geom_point(aes(x = pH, y = CA))+theme_bw(),
ggplot(norway)+geom_point(aes(x = pH, y = OA))+ylim(-1e-4, 1e-4)+theme_bw(),
ggplot(norway)+geom_point(aes(x = TOC, y = OA))+theme_bw(),
ggplot(norway)+geom_point(aes(x = TA, y = OA))+theme_bw(), nrow = 2, ncol = 2)

Figure 5: OA estimated as TA - CA, in eq/L

3.3 Organic alkalinity according to Hruška et al. (2003)

Hruska et al. suggest that the organic alkalinity (OA) can be computed as a triprotic model. OA is the defined as the concentration of organic bases \([RCOO^-]\) in the solution, minus the concentration of organic bases at pH = 4.5, as for an end-point titration. \([RCOO^-]\) depends on three \(pK_a\) that were measured in Hruška et al. (2003):

\[[RCOO^-]=\alpha_1 \times \frac{m \times [TOC]}{3}+ \alpha_2 \times \frac{m \times [TOC]}{3} + \alpha_3 \times \frac{m \times [TOC]}{3}\]

Where α is the ionization fraction of each acid/base couple:

\[\alpha = \frac{[RCOO^-]}{[RCOOH]}=\frac{K_a}{[H^+} = \frac{10^{-pK_a}}{[H^+]}\]

And \(m\) is the site density of carboxylic group on the organic matter:

\[m = 10.2 \; \pm \; 0.6 \; \mu eq/mg \; DOC \Leftrightarrow 0.12 \; eq/mol \; DOC\]

\(m\) is supposed to be equally divided between the three acids with their respective \(pK_a\).

pKa1 <- 3.04
Ka1 <- 10^(-pKa1)

pKa2 <- 4.42
Ka2 <- 10^(-pKa2)

pKa3 <- 6.46
Ka3 <- 10^(-pKa3)

m <- 10.2*1e-6*12.011*1e3*1e-3# ueq/mg to eq/mol, site density BUT THERE IS A 1e3 PB: have to multiply by 1e-3 to stay in the range
norway$RCOO <- with(norway, (Ka1/Hplus + 2*Ka2/Hplus + 3*Ka3/Hplus)* m/3 * TOC) # estimated in eq/L

norway$RCOO_4.5 <- with(norway, (Ka1/10^(-4.5) + 2*Ka2/10^(-4.5) + 3*Ka3/10^(-4.5))* m/3 * TOC)

norway$OA_hruska <- with(norway, RCOO-RCOO_4.5)

ggplot(norway)+
  geom_point(aes(x = pH, y = RCOO, col = survey))+
  scale_color_manual(values = c("firebrick","dodgerblue3"))+
  theme_minimal()+
  theme(legend.position = "bottom")

norway$CA_hruska <- with(norway, TA - OA_hruska - OH + Hplus) 

norway$CO3_hruska <- with(norway,CA_hruska / (Hplus/K2 +2)) # in mol/L
norway$HCO3_hruska <- with(norway, CO3_hruska*Hplus/K2)
norway$H2CO3_hruska <- with(norway, HCO3_hruska*Hplus/K1)
norway$fCO2_hruska <- with(norway,H2CO3_hruska/K0)

Figure 6: OA estimated with triprotic method of Hruska et al., in eq/L

ggplot(norway,aes(x= pH))+geom_point(aes(y = fCO2_hruska, col = "pCO2 from calculated from Hruska et al"), alpha = 0.5)+
  geom_point(aes(y = fCO2, col = "Measured pCO2"), alpha = 0.5)+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

Figure 7: pCO2 estimated with Hruska method, in atm

3.4 Organic alkalinity according to Liu, Butman, and Raymond (2020)

A simplifying approach was suggested by Liu, Butman, and Raymond (2020) , building on Cai, Wang, and Hodson (1998) and Lozovik (2005), where the organic alkalinity can be calculated directly from TOC as:

\(OA = 80 \% \times 10\% \times [TOC]\)

80% being the proportion of DOC that is an organic acid [@Cai1998], and 10% the maximum fraction of anions contributing to alkalinity (Lozovik 2005). This last value was calculated for DOC in humic lakes, but overall this equation is designed to be applicable to all kinds of lakes, tropical or temperate.

#norway$pH_Liu <- with(norway, pH - (0.03+0.05*log10(IS))) 
#norway$Hplus_Liu <- 10^(-norway$pH_Liu) 
#norway$OH_Liu <- with(norway,Kw*Hplus_Liu)

norway$OA_Liu <- 0.08 * norway$TOC
norway$CA_Liu <- with(norway, TA-OA_Liu - OH + Hplus)

norway$CO3_Liu <- with(norway,CA_Liu / (Hplus/K2 +2)) # in mol/L
norway$HCO3_Liu <- with(norway, CO3_Liu*Hplus/K2)
norway$H2CO3_Liu <- with(norway, HCO3_Liu*Hplus/K1)
norway$fCO2_Liu <- with(norway,H2CO3_Liu/K0)

norway$DIC_Liu <- with(norway, H2CO3_Liu + HCO3_Liu + CO3_Liu)

ggplot(norway,aes(x= pH))+geom_point(aes(y = fCO2_Liu, col = "pCO2 from calculated from Liu et al."), alpha = 0.5)+
  geom_point(aes(y = fCO2, col = "Measured pCO2"), alpha = 0.5)+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

Figure 8: pCO2 estimated with Liu method, in atm

4 Model TIC

4.1 Theory

• TIC can be expressed as a function of $TA$ , \([H^+]\) and \(TOC\). First we have to express it depending on \(pCO_2\), \(HCO_3^-\) or \(CO_3^{2-}\).

\(TIC = H_2CO_3 + HCO_3^- + CO_3^{2-}\)

$ K_0 = [H_2CO_3]/ pCO_2 H_2CO_3 = pCO_2 K_0$

$K_1 = = $

\(K_2 = \frac{[CO_3^{2-}] \times [H^+]}{[HCO_3^-]} \Leftrightarrow [CO_3^{2-}] = \frac{[HCO_3^-] \times K_2}{[H^+]}\)

Therefore

\(TIC = pCO_2 \times K_0 \times \left( 1 + \frac{K_1}{H^+} + \frac{K_2K_1}{[H^+]^2} \right)\)

4.2 TA

dic.ta <- glm(formula = DIC~TA, data = norway, family = Gamma(link = "identity"))

dic.ta.sum <- summary(dic.ta)$coefficients %>% as.data.frame() 
dic.ta.sp <- rownames(dic.ta.sum)[which(dic.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.ta.sum <- dic.ta.sum %>% format(scientific = T, digits = 2)

kable(dic.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	4.1e-05	3.3e-06	1.2e+01	2.6e-25
TA	1.3e+00	1.0e-01	1.2e+01	6.7e-25

norway$DIC_pred <- fitted(dic.ta)
norway$DIC_pred_res <- residuals(dic.ta)
dic.ta.r2 <- with(summary(dic.ta), 1 - deviance/null.deviance) %>% round(2)
dic.ta.aic <- AIC(dic.ta)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.ta.r2, ""))+
    theme_minimal(base_size = 15)

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
   coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
  theme_minimal(base_size = 15)

norway$pCO2_calc <- with(norway, DIC_pred/(K0*(1+K1*Hplus+K2*K1*Hplus^2)))

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 9: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA

nlss$dic_pred <- predict(dic.ta, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from modelled DIC"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 10: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.ta <- glm(formula = fCO2~TA+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.ta.sum <- summary(pco2.ta)$coefficients %>% as.data.frame() 
pco2.ta.sp <- rownames(pco2.ta.sum)[which(pco2.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.ta.sum <- pco2.ta.sum %>% format(scientific = T, digits = 2)

kable(pco2.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TA	6.9e+00	1.1e+00	6.3e+00	2.5e-09

norway$pCO2_pred <- fitted(pco2.ta)
norway$pCO2_pred_res <- residuals(pco2.ta)
pco2.ta.r2 <- with(summary(pco2.ta), 1 - deviance/null.deviance) %>% round(2)
pco2.ta.aic <- AIC(pco2.ta)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   
  labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 11: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) predicted (blue) pCO2 vs pH for pCO2~TA

nlss$pCO2_pred <- predict(pco2.ta, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "predicted pCO2 NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 12: Predicted pCO2 in atm vs pH for the Northern Lake Survey

4.3 1/TA

norway$invTA <- with(norway, ifelse(TA == 0, 0, 1/TA))

dic.invTA <- glm(formula = DIC~invTA, data = norway, family = Gamma(link = "identity"))

dic.invTA.sum <- summary(dic.invTA)$coefficients %>% as.data.frame() 
dic.invTA.sp <- rownames(dic.invTA.sum)[which(dic.invTA.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.invTA.sum <- dic.invTA.sum %>% format(scientific = T, digits = 2)

kable(dic.invTA.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	1.8e-04	2.1e-05	8.4e+00	2.0e-14
invTA	-2.5e-10	4.4e-11	-5.8e+00	3.4e-08

norway$DIC_pred <- fitted(dic.invTA)
norway$DIC_pred_res <- residuals(dic.invTA)
dic.invTA.r2 <- with(summary(dic.invTA), 1 - deviance/null.deviance) %>% round(2)
dic.invTA.aic <- AIC(dic.invTA)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.invTA.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
   coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
  theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0*(1+K1*Hplus+K2*K1*Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2, rel_heights = c(2,3), title = "test")

Figure 13: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~1/TA

nlss$invTA <- with(nlss, ifelse(TA == 0, 0, 1/TA))

nlss$dic_pred <- predict(dic.invTA, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from modelled DIC"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 14: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.invTA <- glm(formula = fCO2~invTA+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.invTA.sum <- summary(pco2.invTA)$coefficients %>% as.data.frame() 
pco2.invTA.sp <- rownames(pco2.invTA.sum)[which(pco2.invTA.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.invTA.sum <- pco2.invTA.sum %>% format(scientific = T, digits = 2)

kable(pco2.invTA.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
invTA	2e-08	5.8e-09	3.5e+00	6.7e-04

norway$pCO2_pred <- fitted(pco2.invTA)
norway$pCO2_pred_res <- residuals(pco2.invTA)
pco2.invTA.r2 <- with(summary(pco2.invTA), 1 - deviance/null.deviance) %>% round(2)
pco2.invTA.aic <- AIC(pco2.invTA)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   
  labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.invTA.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 15: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) and predicted (blue) pCO2 vs pH for pCO2~1/TA

nlss$pCO2_pred <- predict(pco2.invTA, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "predicted pCO2 NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 16: Predicted pCO2 in atm vs pH for the Northern Lake Survey

4.5 TA + TOC

dic.toc.ta <- glm(formula = DIC~TOC+TA, data = norway, family = Gamma(link = "identity"))
dic.toc.ta.sum <- summary(dic.toc.ta)$coefficients %>% as.data.frame() 
dic.toc.ta.sp <- rownames(dic.toc.ta.sum)[which(dic.toc.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.toc.ta.sum <- dic.toc.ta.sum %>% format(scientific = T, digits = 2)

kable(dic.toc.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	2.8e-05	3.1e-06	9.1e+00	2.4e-16
TOC	4.0e-02	1.0e-02	3.9e+00	1.2e-04
TA	1.1e+00	1.0e-01	1.1e+01	2.6e-22

norway$DIC_pred <- fitted(dic.toc.ta)
norway$DIC_pred_res <- residuals(dic.toc.ta)
dic.toc.ta.r2 <- with(summary(dic.toc.ta), 1 - deviance/null.deviance) %>% round(2)
dic.toc.ta.aic <- AIC(dic.toc.ta)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.toc.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 22: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA+TOC

nlss$dic_pred <- predict(dic.toc.ta, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 23: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.toc.ta <- glm(formula = fCO2~TOC+TA+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.toc.ta.sum <- summary(pco2.toc.ta)$coefficients %>% as.data.frame() 
pco2.toc.ta.sp <- rownames(pco2.toc.ta.sum)[which(pco2.toc.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.toc.ta.sum <- pco2.toc.ta.sum %>% format(scientific = T, digits = 2)

kable(pco2.toc.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	9.3e-01	8.6e-02	1.1e+01	7.0e-21
TA	8.7e-01	4.8e-01	1.8e+00	7.5e-02

norway$pCO2_pred <- fitted(pco2.toc.ta)
norway$pCO2_pred_res <- residuals(pco2.toc.ta)
pco2.toc.ta.r2 <- with(summary(pco2.toc.ta), 1 - deviance/null.deviance) %>% round(2)
pco2.toc.ta.aic <- AIC(pco2.toc.ta)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.toc.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 24: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for pCO2~TOC+TA `

nlss$pCO2_pred <- predict(pco2.toc.ta, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 25: Predicted pCO2 in atm vs pH for the Northern Lake Survey

4.6 TA*TOC + Hplus

dic.tocta.Hplus <- glm(formula = DIC~TOC+TA+Hplus, data = norway, family = Gamma(link = "identity"))
  dic.tocta.Hplus.sum <- summary(dic.tocta.Hplus)$coefficients %>% as.data.frame() 
  dic.tocta.Hplus.sp <- rownames(dic.tocta.Hplus.sum)[which(dic.tocta.Hplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
  dic.tocta.Hplus.sum <- dic.tocta.Hplus.sum %>% format(scientific = T, digits = 2)

kable(dic.tocta.Hplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	2.0e-05	3.7e-06	5.3e+00	4.0e-07
TOC	1.7e-02	1.1e-02	1.5e+00	1.3e-01
TA	1.3e+00	1.2e-01	1.1e+01	8.9e-22
Hplus	3.0e+00	8.7e-01	3.4e+00	7.5e-04

norway$DIC_pred <- fitted(dic.tocta.Hplus)
norway$DIC_pred_res <- residuals(dic.tocta.Hplus)
dic.tocta.Hplus.r2 <- with(summary(dic.tocta.Hplus), 1 - deviance/null.deviance) %>% round(2)
dic.tocta.Hplus.aic <- AIC(dic.tocta.Hplus)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.tocta.Hplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 26: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA x TOC + Hplus

nlss$dic_pred <- predict(dic.tocta.Hplus, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 27: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.tocta.Hplus <- glm(formula = fCO2~TOC+TA+Hplus+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.tocta.Hplus.sum <- summary(pco2.tocta.Hplus)$coefficients %>% as.data.frame() 
pco2.tocta.Hplus.sp <- rownames(pco2.tocta.Hplus.sum)[which(pco2.tocta.Hplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.tocta.Hplus.sum <- pco2.tocta.Hplus.sum %>% format(scientific = T, digits = 2)

kable(pco2.tocta.Hplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	7.1e-01	9.7e-02	7.3e+00	1.1e-11
TA	1.6e+00	5.3e-01	3.0e+00	3.5e-03
Hplus	2.7e+01	8.0e+00	3.3e+00	1.1e-03

norway$pCO2_pred <- fitted(pco2.tocta.Hplus)
norway$pCO2_pred_res <- residuals(pco2.tocta.Hplus)
pco2.tocta.Hplus.r2 <- with(summary(pco2.tocta.Hplus), 1 - deviance/null.deviance) %>% round(2)
pco2.tocta.Hplus.aic <- AIC(pco2.tocta.Hplus)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.tocta.Hplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 28: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for pCO2~TA x TOC + Hplus

nlss$pCO2_pred <- predict(pco2.tocta.Hplus, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 29: Predicted pCO2 in atm vs pH for the Northern Lake Survey

4.7 TOC + pH

dic.toc.Hplus <- glm(formula = DIC~TOC+Hplus, data = norway, family = Gamma(link = "identity"))
dic.toc.Hplus.sum <- summary(dic.toc.Hplus)$coefficients %>% as.data.frame() 
dic.toc.Hplus.sp <- rownames(dic.toc.Hplus.sum)[which(dic.toc.Hplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.toc.Hplus.sum <- dic.toc.Hplus.sum %>% format(scientific = T, digits = 2)

kable(dic.toc.Hplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	3.9e-05	9.7e-06	4.0e+00	9.4e-05
TOC	2.3e-01	3.0e-02	7.7e+00	1.1e-12
Hplus	-5.2e+00	1.7e+00	-3.1e+00	2.7e-03

norway$DIC_pred <- fitted(dic.toc.Hplus)
norway$DIC_pred_res <- residuals(dic.toc.Hplus)
dic.toc.Hplus.r2 <- with(summary(dic.toc.Hplus), 1 - deviance/null.deviance) %>% round(2)
dic.toc.Hplus.aic <- AIC(dic.toc.Hplus)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.toc.Hplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "Hplus", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 30: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TOC+Hplus

nlss$dic_pred <- predict(dic.toc.Hplus, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 31: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.toc.Hplus <- glm(formula = fCO2~TOC+Hplus+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.toc.Hplus.sum <- summary(pco2.toc.Hplus)$coefficients %>% as.data.frame() 
pco2.toc.Hplus.sp <- rownames(pco2.toc.Hplus.sum)[which(pco2.toc.Hplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.toc.Hplus.sum <- pco2.toc.Hplus.sum %>% format(scientific = T, digits = 2)

kable(pco2.toc.Hplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	9.9e-01	6.7e-02	1.5e+01	5.7e-32
Hplus	1.5e+01	7.5e+00	2.1e+00	4.1e-02

norway$pCO2_pred <- fitted(pco2.toc.Hplus)
norway$pCO2_pred_res <- residuals(pco2.toc.Hplus)
pco2.toc.Hplus.r2 <- with(summary(pco2.toc.Hplus), 1 - deviance/null.deviance) %>% round(2)
pCO2.toc.Hplus.aic <- AIC(pco2.toc.Hplus)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.toc.Hplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 30: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TOC+Hplus

nlss$pCO2_pred <- predict(pco2.toc.Hplus, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 32: Predicted pCO2 in atm vs pH for the Northern Lake Survey

4.8 TA * TOC

dic.tocta <- glm(formula = DIC~TOC*TA, data = norway, family = Gamma(link = "identity"))
dic.tocta.sum <- summary(dic.tocta)$coefficients %>% as.data.frame() 
dic.tocta.sp <- rownames(dic.tocta.sum)[which(dic.toc.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.tocta.sum <- dic.tocta.sum %>% format(scientific = T, digits = 2)

kable(dic.tocta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	2.9e-05	3.4e-06	8.6e+00	7.0e-15
TOC	3.8e-02	1.1e-02	3.5e+00	6.5e-04
TA	1.0e+00	1.6e-01	6.6e+00	4.7e-10
TOC:TA	1.2e+02	1.7e+02	7.1e-01	4.8e-01

norway$DIC_pred <- fitted(dic.tocta)
norway$DIC_pred_res <- residuals(dic.tocta)
dic.tocta.r2 <- with(summary(dic.tocta), 1 - deviance/null.deviance) %>% round(2)
dic.tocta.aic <- AIC(dic.tocta)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.tocta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2", size = DIC))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 33: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA x TOC

nlss$dic_pred <- predict(dic.tocta, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS", size = dic_pred), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 34: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.tocta <- glm(formula = fCO2~TOC+TA+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.tocta.sum <- summary(pco2.tocta)$coefficients %>% as.data.frame() 
pco2.tocta.sp <- rownames(pco2.tocta.sum)[which(pco2.tocta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.tocta.sum <- pco2.tocta.sum %>% format(scientific = T, digits = 2)

kable(pco2.tocta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	9.3e-01	8.6e-02	1.1e+01	7.0e-21
TA	8.7e-01	4.8e-01	1.8e+00	7.5e-02

norway$pCO2_pred <- fitted(pco2.tocta)
norway$pCO2_pred_res <- residuals(pco2.tocta)
pco2.tocta.r2 <- with(summary(pco2.tocta), 1 - deviance/null.deviance) %>% round(2)
pco2.tocta.aic <- AIC(pco2.tocta)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.tocta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 35: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for pCO2~TA x TOC

nlss$pCO2_pred <- predict(pco2.tocta, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 36: Predicted pCO2 in atm vs pH for the Northern Lake Survey

4.9 TA*Hplus

dic.taHplus <- glm(formula = DIC~TA*Hplus, data = norway, family = Gamma(link = "identity"))

dic.taHplus.sum <- summary(dic.taHplus)$coefficients %>% as.data.frame() 
dic.taHplus.sp <- rownames(dic.taHplus.sum)[which(dic.taHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.taHplus.sum <- dic.taHplus.sum %>% format(scientific = T, digits = 2)

kable(dic.taHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	1.8e-05	3.9e-06	4.7e+00	5.3e-06
TA	1.4e+00	9.9e-02	1.4e+01	1.4e-30
Hplus	4.0e+00	7.8e-01	5.1e+00	9.1e-07
TA:Hplus	1.1e+05	1.1e+05	9.9e-01	3.3e-01

norway$DIC_pred <- fitted(dic.taHplus)
norway$DIC_pred_res <- residuals(dic.taHplus)
dic.taHplus.r2 <- with(summary(dic.taHplus), 1 - deviance/null.deviance) %>% round(2)
dic.taHplus.aic <- AIC(dic.taHplus)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.taHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 37: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA x Hplus

nlss$dic_pred <- predict(dic.taHplus, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 38: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.taHplus <- glm(formula = fCO2~TA*Hplus+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.taHplus.sum <- summary(pco2.taHplus)$coefficients %>% as.data.frame() 
pco2.taHplus.sp <- rownames(pco2.taHplus.sum)[which(pco2.taHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.taHplus.sum <- pco2.taHplus.sum %>% format(scientific = T, digits = 2)

kable(pco2.taHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TA	3.0e+00	3.8e-01	7.9e+00	3.5e-13
Hplus	5.3e+01	6.8e+00	7.7e+00	1.2e-12
TA:Hplus	9.0e+06	1.3e+06	7.1e+00	4.2e-11

norway$pCO2_pred <- fitted(pco2.taHplus)
norway$pCO2_pred_res <- residuals(pco2.taHplus)
pco2.taHplus.r2 <- with(summary(pco2.taHplus), 1 - deviance/null.deviance) %>% round(2)
pco2.taHplus.aic <- AIC(pco2.taHplus)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.taHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 39: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA

nlss$pCO2_pred <- predict(pco2.taHplus, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 40: Predicted pCO2 in atm vs pH for the Northern Lake Survey

4.10 TOC*Hplus

dic.TOCHplus <- glm(formula = DIC~TOC*Hplus, data = norway, family = Gamma(link = "identity"))

dic.TOCHplus.sum <- summary(dic.TOCHplus)$coefficients %>% as.data.frame() 
dic.TOCHplus.sp <- rownames(dic.TOCHplus.sum)[which(dic.TOCHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.TOCHplus.sum <- dic.TOCHplus.sum %>% format(scientific = T, digits = 2)

kable(dic.TOCHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	2.7e-05	9.5e-06	2.9e+00	4.5e-03
TOC	2.6e-01	3.4e-02	7.7e+00	1.1e-12
Hplus	-1.6e+00	2.3e+00	-7.1e-01	4.8e-01
TOC:Hplus	-8.6e+03	4.7e+03	-1.8e+00	6.7e-02

norway$DIC_pred <- fitted(dic.TOCHplus)
norway$DIC_pred_res <- residuals(dic.TOCHplus)
dic.TOCHplus.r2 <- with(summary(dic.TOCHplus), 1 - deviance/null.deviance) %>% round(2)
dic.TOCHplus.aic <- AIC(dic.TOCHplus)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.TOCHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 41: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TOC x Hplus

nlss$dic_pred <- predict(dic.TOCHplus, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 42: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.TOCHplus <- glm(formula = fCO2~TOC*Hplus+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.TOCHplus.sum <- summary(pco2.TOCHplus)$coefficients %>% as.data.frame() 
pco2.TOCHplus.sp <- rownames(pco2.TOCHplus.sum)[which(pco2.TOCHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.TOCHplus.sum <- pco2.TOCHplus.sum %>% format(scientific = T, digits = 2)

kable(pco2.TOCHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	9.9e-01	7.0e-02	1.4e+01	2.2e-30
Hplus	1.6e+01	1.1e+01	1.5e+00	1.4e-01
TOC:Hplus	-2.3e+03	2.4e+04	-9.6e-02	9.2e-01

norway$pCO2_pred <- fitted(pco2.TOCHplus)
norway$pCO2_pred_res <- residuals(pco2.TOCHplus)
pco2.TOCHplus.r2 <- with(summary(pco2.TOCHplus), 1 - deviance/null.deviance) %>% round(2)
pco2.TOCHplus.aic <- AIC(pco2.TOCHplus)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.TOCHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 41: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TOC x Hplus

nlss$pCO2_pred <- predict(pco2.TOCHplus, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 42: Predicted pCO2 in atm vs pH for the Northern Lake Survey

4.11 TA + TOC*Hplus

dic.tocHplus.ta <- glm(formula = DIC~TOC*Hplus+TA, data = norway, family = Gamma(link = "identity"))
dic.tocHplus.ta.sum <- summary(dic.tocHplus.ta)$coefficients %>% as.data.frame() 
dic.tocHplus.ta.sp <- rownames(dic.tocHplus.ta.sum)[which(dic.tocHplus.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.tocHplus.ta.sum <- dic.tocHplus.ta.sum %>% format(scientific = T, digits = 2)

kable(dic.tocHplus.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	2.4e-05	4.5e-06	5.3e+00	4.0e-07
TOC	-3.1e-05	1.4e-02	-2.3e-03	1.0e+00
Hplus	1.6e+00	1.2e+00	1.3e+00	2.0e-01
TA	1.4e+00	1.2e-01	1.1e+01	7.3e-22
TOC:Hplus	3.7e+03	2.3e+03	1.6e+00	1.1e-01

norway$DIC_pred <- fitted(dic.tocHplus.ta)
norway$DIC_pred_res <- residuals(dic.tocHplus.ta)
dic.tocHplus.ta.r2 <- with(summary(dic.tocHplus.ta), 1 - deviance/null.deviance) %>% round(2)
dic.tocHplus.ta.aic <- AIC(dic.tocHplus.ta)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.tocHplus.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 43: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC ~ TA + TOC x Hplus

nlss$dic_pred <- predict(dic.tocHplus.ta, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 44: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.tocHplus.ta <- glm(formula = fCO2~TOC*Hplus+TA+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.tocHplus.ta.sum <- summary(pco2.tocHplus.ta)$coefficients %>% as.data.frame() 
pco2.tocHplus.ta.sp <- rownames(pco2.tocHplus.ta.sum)[which(pco2.tocHplus.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.tocHplus.ta.sum <- pco2.tocHplus.ta.sum %>% format(scientific = T, digits = 2)

kable(pco2.tocHplus.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	6.3e-01	1.1e-01	6.0e+00	1.6e-08
Hplus	1.7e+01	1.1e+01	1.6e+00	1.1e-01
TA	1.9e+00	5.6e-01	3.3e+00	1.0e-03
TOC:Hplus	4.0e+04	2.6e+04	1.5e+00	1.3e-01

norway$pCO2_pred <- fitted(pco2.tocHplus.ta)
norway$pCO2_pred_res <- residuals(pco2.tocHplus.ta)
pco2.tocHplus.ta.r2 <- with(summary(pco2.tocHplus.ta), 1- deviance/null.deviance) %>% round(2)
pco2.tocHplus.ta.aic <- AIC(pco2.tocHplus.ta)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.tocHplus.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 43: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC ~ TA + TOC x Hplus

nlss$pCO2_pred <- predict(pco2.tocHplus.ta, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 44: Predicted pCO2 in atm vs pH for the Northern Lake Survey

4.12 TOC + TA*Hplus

dic.toc.taHplus <- glm(formula = DIC~TOC+TA*Hplus, data = norway, family = Gamma(link = "identity"))

dic.toc.taHplus.sum <- summary(dic.toc.taHplus)$coefficients %>% as.data.frame() 
dic.toc.taHplus.sp <- rownames(dic.toc.taHplus.sum)[which(dic.toc.taHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.toc.taHplus.sum <- dic.toc.taHplus.sum %>% format(scientific = T, digits = 2)
kable(dic.toc.taHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	2.0e-05	3.8e-06	5.2e+00	6.7e-07
TOC	1.7e-02	1.3e-02	1.3e+00	2.0e-01
TA	1.3e+00	1.2e-01	1.1e+01	1.5e-21
Hplus	3.0e+00	9.1e-01	3.2e+00	1.4e-03
TA:Hplus	-4.5e+03	1.1e+05	-3.9e-02	9.7e-01

norway$DIC_pred <- fitted(dic.toc.taHplus)
norway$DIC_pred_res <- residuals(dic.toc.taHplus)
dic.toc.taHplus.r2 <- with(summary(dic.toc.taHplus), 1 - deviance/null.deviance) %>% round(2)
dic.toc.taHplus.aic <- AIC(dic.toc.taHplus)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.toc.taHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 9: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA

nlss$dic_pred <- predict(dic.toc.taHplus, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 45: Predicted pCO2 in atm vs pH for the Northern Lake Survey

pco2.toc.taHplus <- glm(formula = fCO2~TOC+TA*Hplus+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.toc.taHplus.sum <- summary(pco2.toc.taHplus)$coefficients %>% as.data.frame()
pco2.toc.taHplus.sp <- rownames(pco2.toc.taHplus.sum)[which(pco2.toc.taHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.toc.taHplus.sum <- pco2.toc.taHplus.sum %>% format(scientific = T, digits = 2)

kable(pco2.toc.taHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	3.0e-01	1.0e-01	2.9e+00	4.4e-03
TA	2.1e+00	4.8e-01	4.5e+00	1.4e-05
Hplus	3.8e+01	7.4e+00	5.2e+00	5.6e-07
TA:Hplus	6.0e+06	1.5e+06	4.1e+00	7.7e-05

norway$pCO2_pred <- fitted(pco2.toc.taHplus)
norway$pCO2_pred_res <- residuals(pco2.toc.taHplus)
pco2.toc.taHplus.r2 <- with(summary(pco2.toc.taHplus), 1 - deviance/null.deviance) %>% round(2)
pco2.toc.taHplus.aic <- AIC(pco2.toc.taHplus)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.toc.taHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 46: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for pCO2~TOC + TA x Hplus

nlss$pCO2_pred <- predict(pco2.toc.taHplus, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 47: Predicted pCO2 in atm vs pH for the Northern Lake Survey

4.13 TOC + TA*invHplus

norway$invHplus <- with(norway, 1/Hplus)

dic.toc.tainvHplus <- glm(formula = DIC~TOC+TA*invHplus, data = norway, family = Gamma(link = "identity"))

dic.toc.tainvHplus.sum <- summary(dic.toc.tainvHplus)$coefficients %>% as.data.frame()
dic.toc.tainvHplus.sp <- rownames(dic.toc.tainvHplus.sum)[which(dic.toc.tainvHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.toc.tainvHplus.sum <- dic.toc.tainvHplus.sum %>% format(scientific = T, digits = 2)

kable(dic.toc.tainvHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	3.4e-05	2.6e-06	1.3e+01	7.8e-28
TOC	4.9e-02	7.6e-03	6.4e+00	1.6e-09
TA	4.0e-01	1.1e-01	3.5e+00	5.1e-04
invHplus	-5.6e-12	2.0e-12	-2.8e+00	5.0e-03
TA:invHplus	1.0e-07	1.4e-08	7.4e+00	7.0e-12

norway$DIC_pred <- fitted(dic.toc.tainvHplus)
norway$DIC_pred_res <- residuals(dic.toc.tainvHplus)
dic.toc.tainvHplus.r2 <- with(summary(dic.toc.tainvHplus), 1 - deviance/null.deviance) %>% round(2)
dic.toc.tainvHplus.aic <- AIC(dic.toc.tainvHplus)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.toc.tainvHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 48: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TOC + TA/hplus

nlss$dic_pred <- predict(dic.toc.tainvHplus, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 49: Predicted pCO2 in atm vs pH for the Northern Lake Survey

norway$invHplus <- with(norway, 1/Hplus)

pco2.toc.tainvHplus <- glm(formula = fCO2~TOC+TA*invHplus+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.toc.tainvHplus.sum <- summary(pco2.toc.tainvHplus)$coefficients %>% as.data.frame() 
pco2.toc.tainvHplus.sp <- rownames(pco2.toc.tainvHplus.sum)[which(pco2.toc.tainvHplus.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.toc.tainvHplus.sum <- pco2.toc.tainvHplus.sum %>% format(scientific = T, digits = 2)

kable(pco2.toc.tainvHplus.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	9.8e-01	9.1e-02	1.1e+01	8.8e-21
TA	8.0e-01	8.2e-01	9.6e-01	3.4e-01
invHplus	-3.4e-11	6.6e-12	-5.1e+00	9.0e-07
TA:invHplus	1.5e-07	5.3e-08	2.8e+00	6.1e-03

norway$pCO2_pred <- fitted(pco2.toc.tainvHplus)
norway$pCO2_pred_res <- residuals(pco2.toc.tainvHplus)
pco2.toc.tainvHplus.r2 <- with(summary(pco2.toc.tainvHplus), 1 - deviance / null.deviance) %>% round(2)
pco2.toc.tainvHplus.aic <- AIC(pco2.toc.tainvHplus)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.toc.tainvHplus.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
   coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

*Figure 9: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC~TA

nlss$pCO2_pred <- predict(pco2.toc.tainvHplus, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 50: Predicted pCO2 in atm vs pH for the Northern Lake Survey

4.14 TA + TOC*invHplus

norway$invHplus <- with(norway, 1/Hplus)

dic.tocinvHplus.ta <- glm(formula = DIC~TOC*invHplus+TA, data = norway, family = Gamma(link = "identity"))

dic.tocinvHplus.ta.sum <- summary(dic.tocinvHplus.ta)$coefficients %>% as.data.frame() 
dic.tocinvHplus.ta.sp <- rownames(dic.tocinvHplus.ta.sum)[which(dic.tocinvHplus.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
dic.tocinvHplus.ta.sum <- dic.tocinvHplus.ta.sum %>% format(scientific = T, digits = 2)

kable(dic.tocinvHplus.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	2.9e-05	3.1e-06	9.3e+00	9.7e-17
TOC	4.6e-02	9.5e-03	4.9e+00	2.8e-06
invHplus	2.9e-12	2.6e-12	1.1e+00	2.6e-01
TA	3.8e-01	1.5e-01	2.5e+00	1.4e-02
TOC:invHplus	1.6e-08	4.1e-09	3.9e+00	1.3e-04

norway$DIC_pred <- fitted(dic.tocinvHplus.ta)
norway$DIC_pred_res <- residuals(dic.tocinvHplus.ta)
dic.tocinvHplus.ta.r2 <- with(summary(dic.tocinvHplus.ta), 1 - deviance/null.deviance) %>% round(2)
dic.tocinvHplus.ta.aic <- AIC(dic.tocinvHplus.ta)

g1 <- ggplot(norway)+geom_point(aes(x=DIC,y=DIC_pred))+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",dic.tocinvHplus.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=DIC_pred,y=DIC_pred_res))+   
    coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()

norway$pCO2_calc <- with(norway, DIC_pred/(K0+K0*K1/Hplus+K0*K1*K2/(Hplus^2)))


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_calc, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3+labs(caption = ),nrow = 2,rel_heights = c(2,3))

Figure 51: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for DIC ~ TOC / Hplus + TA

nlss$dic_pred <- predict(dic.tocinvHplus.ta, newdata = nlss, type = "response")
nlss$pCO2_calc <- with(nlss, dic_pred/(K0+K0*K1/Hplus+K0*K1*K2/Hplus))

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_calc, col = "pCO2 from predicted DIC, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 52: Predicted pCO2 in atm vs pH for the Northern Lake Survey

norway$invHplus <- with(norway, 1/Hplus)

pco2.tocinvHplus.ta <- glm(formula = fCO2~TOC*invHplus+TA+0+offset(fCO2.atm), data = norway, family = Gamma(link = "identity"))

pco2.tocinvHplus.ta.sum <- summary(pco2.tocinvHplus.ta)$coefficients %>% as.data.frame() 
pco2.tocinvHplus.ta.sp <- rownames(pco2.tocinvHplus.ta.sum)[which(pco2.tocinvHplus.ta.sum$`Pr(>|t|)` < 0.05)] %>% paste(collapse = ", ")
pco2.tocinvHplus.ta.sum <- pco2.tocinvHplus.ta.sum %>% format(scientific = T, digits = 2)
  

kable(pco2.tocinvHplus.ta.sum, digits = 2) %>% kable_styling(bootstrap_options = "bordered")

	Estimate	Std. Error	t value	Pr(>|t|)
TOC	9.0e-01	8.7e-02	1.0e+01	1.3e-19
invHplus	-1.6e-11	7.9e-12	-2.1e+00	3.9e-02
TA	2.2e+00	7.8e-01	2.8e+00	6.4e-03
TOC:invHplus	-4.3e-09	1.3e-08	-3.2e-01	7.5e-01

norway$pCO2_pred <- fitted(pco2.tocinvHplus.ta)
norway$pCO2_pred_res <- residuals(pco2.tocinvHplus.ta)
pco2.tocinvHplus.ta.r2 <- with(summary(pco2.tocinvHplus.ta), 1 - deviance/null.deviance) %>% round(2)
pco2.tocinvHplus.ta.aic <- AIC(pco2.tocinvHplus.ta)

g1 <- ggplot(norway)+geom_point(aes(x=fCO2,y=pCO2_pred))+   labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  labs(x = "Measured pCO2, atm", y = "Predicted pCO2, atm")+
  geom_abline(slope= 1, intercept = 0)+coord_trans(x="log10",y="log10")+
  annotate(x = 0.5e-3, y = 3e-3, geom = "label", label = paste("R2 = ",pco2.tocinvHplus.ta.r2, ""))+
    theme_minimal()

g2 <- ggplot(norway)+geom_point(aes(x=pCO2_pred,y=pCO2_pred_res))+
     coord_trans(x = "log10")+labs(x = "fitted", y = "Std Residuals")+
    theme_minimal()


g3 <- ggplot(norway,aes(x= pH))+geom_point(aes(y = pCO2_pred, col = "pCO2 from model"))+
  geom_point(aes(y = fCO2, col = "Measured pCO2"))+
  labs(y = "pCO2, atm", x = "pH", col = "")+
  scale_color_manual(values = c( "firebrick","dodgerblue3"))+
  facet_grid(cols = vars(survey))+
  theme_minimal()+
  theme(legend.position = "bottom")

plot_grid(ggarrange(g1,g2),g3,nrow = 2,rel_heights = c(2,3))

Figure 53: Predicted vs fitted values, Standardized residuals vs fitted values,and measured (red) calculated (blue) pCO2 vs pH for pCO2 ~ TOC / Hplus + TA

nlss$pCO2_pred <- predict(pco2.tocinvHplus.ta, newdata = nlss, type = "response")

ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_pred, col = "Predicted pCO2, NLS"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

Figure 36: Predicted pCO2 in atm vs pH for the Northern Lake Survey

4.15 Tableau recap

Table 1: Summary of DIC and pCO2 models

kable(cbind(data.frame(Predictors = c("TA",
                                      "1/TA",
                                "TOC",
                                "TA + TOC",
                                "TA*TOC",
                                "TA*Hplus",
                                "TOC*Hplus",
                                "TA*Hplus + TOC", 
                                "TA + TOC*Hplus",
                                "TA/Hplus + TOC",
                                "TA + TOC/Hplus"),
                        R2 = c(pco2.ta.r2,
                              pco2.invTA.r2,
                              pco2.toc.r2,
                              pco2.toc.ta.r2,
                              pco2.tocta.r2,
                              pco2.taHplus.r2,
                              pco2.TOCHplus.r2,
                              pco2.toc.taHplus.r2,
                              pco2.tocHplus.ta.r2,
                              pco2.toc.tainvHplus.r2,
                              pco2.tocinvHplus.ta.r2),
                       AIC = c(pco2.ta.aic,
                              pco2.invTA.aic,
                              pco2.toc.aic,
                              pco2.toc.ta.aic,
                              pco2.tocta.aic,
                              pco2.taHplus.aic,
                              pco2.TOCHplus.aic,
                              pco2.toc.taHplus.aic,
                              pco2.tocHplus.ta.aic,
                              pco2.toc.tainvHplus.aic,
                              pco2.tocinvHplus.ta.aic),
                        significant  = c(pco2.ta.sp,
                                 pco2.invTA.sp,
                                 pco2.toc.sp,
                                 pco2.toc.ta.sp,
                                 pco2.tocta.sp,
                                 pco2.taHplus.sp,
                                 pco2.TOCHplus.sp,
                                 pco2.toc.taHplus.sp,
                                 pco2.tocHplus.ta.sp,
                                 pco2.toc.tainvHplus.sp,
                                 pco2.tocinvHplus.ta.sp)),
                data.frame(R2 = c(dic.ta.r2,
                                dic.invTA.r2,
                                dic.toc.r2,
                                dic.toc.ta.r2,
                                dic.tocta.r2,
                                dic.taHplus.r2,
                                dic.TOCHplus.r2,
                                dic.toc.taHplus.r2,
                                dic.tocHplus.ta.r2,
                                dic.toc.tainvHplus.r2,
                                dic.tocinvHplus.ta.r2),
                           AIC = c(dic.ta.aic,
                                dic.invTA.aic,
                                dic.toc.aic,
                                dic.toc.ta.aic,
                                dic.tocta.aic,
                                dic.taHplus.aic,
                                dic.TOCHplus.aic,
                                dic.toc.taHplus.aic,
                                dic.tocHplus.ta.aic,
                                dic.toc.tainvHplus.aic,
                                dic.tocinvHplus.ta.aic),
                      significant  = c(dic.ta.sp,
                                dic.invTA.sp,
                                dic.toc.sp,
                                dic.toc.ta.sp,
                                dic.tocta.sp,
                                dic.taHplus.sp,
                                dic.TOCHplus.sp,
                                dic.toc.taHplus.sp,
                                dic.tocHplus.ta.sp,
                                dic.toc.tainvHplus.sp,
                                dic.tocinvHplus.ta.sp))),
             digits = 2) %>% 
  add_header_above(c(" "= 1, "pCO2" = 3, "DIC" = 3),italic = T) %>%
  column_spec(column = c(2,4), bold = T) %>% 
  kable_styling(bootstrap_options = "bordered")

	pCO2			DIC
Predictors	R2	AIC	significant	R2	AIC	significant
TA	0.70	-1971.79	TA	0.78	-2822.02	(Intercept), TA
1/TA	0.18	-1784.04	invTA	0.09	-2562.08	(Intercept), invTA
TOC	0.89	-2147.41	TOC	0.46	-2659.48	(Intercept), TOC
TA + TOC	0.89	-2150.09	TOC	0.82	-2848.87	(Intercept), TOC, TA
TA*TOC	0.89	-2150.09	TOC	0.82	-2847.48
TA*Hplus	0.91	-2169.79	TA, Hplus, TA:Hplus	0.83	-2859.38	(Intercept), TA, Hplus
TOC*Hplus	0.89	-2148.63	TOC	0.51	-2673.35	(Intercept), TOC
TA*Hplus + TOC	0.91	-2174.23	TOC, TA, Hplus, TA:Hplus	0.83	-2859.21	(Intercept), TA, Hplus
TA + TOC*Hplus	0.90	-2161.53	TOC, TA	0.83	-2862.14	(Intercept), TA
TA/Hplus + TOC	0.90	-2159.38	TOC, invHplus, TA:invHplus	0.90	-2939.91	(Intercept), TOC, TA, invHplus, TA:invHplus
TA + TOC/Hplus	0.89	-2149.30	TOC, invHplus, TA	0.86	-2885.38	(Intercept), TOC, TA, TOC:invHplus

5 Northern European Lakes Survey

g1 <- ggplot()+geom_boxplot(data = nlss, aes(x="TA\nNorthern European Lakes Survey, 1995", y=TA, col = "NLS_1995"))+
  geom_boxplot(data = norway, aes(x = "TA\n CBA (2019) and N112 (2004) surveys", y = TA, col = survey))+
  scale_color_manual(values = c("firebrick","orange","dodgerblue"))+
  labs(x = "", col = "",y = "Total alkalinity, eq/L")+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

g2 <- ggplot()+geom_boxplot(data = nlss, aes(x="TOC\nNorthern European Lakes Survey, 1995", y=TOC, col = "NLS_1995"))+
  geom_boxplot(data = norway, aes(x = "TOC\n CBA (2019) and N112 (2004) surveys", y = TOC, col = survey))+
  scale_color_manual(values = c("firebrick","orange","dodgerblue"))+
  labs(x = "", col = "",y = "Total organic carbon, mol/L")+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

g3 <- ggplot()+geom_boxplot(data = nlss, aes(x="pH\nNorthern European Lakes Survey, 1995", y=pH, col = "NLS_1995"))+
  geom_boxplot(data = norway, aes(x = "pH\n CBA (2019) and N112 (2004) surveys", y = pH, col = survey))+
  scale_color_manual(values = c("firebrick","orange","dodgerblue"))+
  labs(x = "", col = "",y = "pH")+
  theme_minimal(base_size = 15)+
  theme(legend.position = "bottom")

ggarrange(g1,g2,g3, common.legend = T, nrow = 3)

nlss$ta_CO3 <- with(nlss,(TA - OH + Hplus) / (Hplus/K2 +2)) # in mol/L
nlss$ta_HCO3 <- with(nlss, ta_CO3*Hplus/K2)
nlss$ta_H2CO3 <- with(nlss, ta_HCO3*Hplus/K1)
nlss$pCO2_ta <- with(nlss,ta_H2CO3/K0)

g1 <- ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_ta), alpha = 0.5, col = "firebrick")+
  labs(x = "pH", y = "pCO2 from TA, atm")+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  facet_zoom(y = pCO2_ta > 0, zoom.size = 1)+
  theme_bw(base_size = 15)

nlss$pCO2_toc <- predict(pco2.toc, newdata = nlss, type = "response")

g1 <- ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_ta, col = "pCO2 from carbonate equilibrium"), alpha = 0.5)+
  geom_point(aes(y = pCO2_toc, col = "pCO2 modelled with TOC"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "")+
  scale_color_manual(values = c("firebrick","dodgerblue"))+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")+
  facet_zoom(y = pCO2_ta > 0, zoom.size = 2)


g2 <- ggplot(data = nlss, aes(x = pH))+
  geom_point(aes(y = pCO2_ta, col = "pCO2 from carbonate equilibrium"), alpha = 0.5)+
  geom_point(aes(y = pCO2_toc, col = "pCO2 modelled with TOC"), alpha = 0.5)+
  geom_hline(yintercept = fCO2.atm.1995, lty = 2)+
  labs(x = "pH", col = "", y = "pCO2, atm")+
  scale_color_manual(values = c("firebrick","dodgerblue"))+
  ylim(0,0.006)+
  theme_bw(base_size = 15)+
  theme(legend.position = "top")

ggarrange(g2,g1, common.legend = T)

temp_k <- 4+273.5 # temperature 4 degrees

K0 <- exp(-58.0931+90.5069*100/temp_k+22.2940*log(temp_k/100)) # Weiss 1974
K1 <- 10^-((3404.71/temp_k)- 14.8435 + 0.032786*temp_k) # Harned and Davis, 1943
K2 <- 10^-((2902.39/temp_k) - 6.4980 + 0.02379*temp_k) # Harned and Scholes, 1941

test <- data.frame(pH = seq(from = 3, to = 10, by = 0.1))
test$Hplus <- 10^(-test$pH)
DIC_1 <- rep(1,71) # mol/L
test$pCO2_1 <- with(test,DIC_1/(K0+K1*K0/Hplus+K0*K1*K2/(Hplus^2)))
test$H2CO3_1 <- with(test,pCO2_1*K0)
test$HCO3_1 <- with(test, K1*H2CO3_1/Hplus)
test$CO3_1 <- with(test,K2*HCO3_1/Hplus)

DIC_2 <- rep(2,71) # mol/L
test$pCO2_2 <- with(test,DIC_2/(K0+K1*K0/Hplus+K0*K1*K2/(Hplus^2)))
test$H2CO3_2 <- with(test,pCO2_2*K0)
test$HCO3_2 <- with(test, K1*H2CO3_2/Hplus)
test$CO3_2 <- with(test,K2*HCO3_2/Hplus)

DIC_3 <- rep(3,71) # mol/L
test$pCO2_3 <- with(test,DIC_3/(K0+K1*K0/Hplus+K0*K1*K2/(Hplus^2)))
test$H2CO3_3 <- with(test,pCO2_3*K0)
test$HCO3_3 <- with(test, K1*H2CO3_3/Hplus)
test$CO3_3 <- with(test,K2*HCO3_3/Hplus)

ggplot(test, aes(x=pH))+geom_point(aes(y=H2CO3_1, col = "DIC = 1"))+
  geom_point(aes(y=H2CO3_2, col = "DIC = 2"))+
  geom_point(aes(y=H2CO3_3, col = "DIC = 3"))+
  scale_color_manual(values = c("firebrick","orange","dodgerblue"))+
  geom_vline(xintercept = -log10(K1))+
  geom_vline(xintercept = -log10(K2))+
  theme_minimal()

6 Evasion rate of CO2

6.1 Theory

Wind speed https://wcrp-cmip.github.io/CMIP6_CVs/docs/CMIP6_institution_id.html

Data downloaded from Copernicus https://cds.climate.copernicus.eu/cdsapp#!/dataset/derived-near-surface-meteorological-variables?tab=overview

See part 1

Theory from Hastie et al. (2018)

\[FCO_2 = A_{lake}*k*\Delta CO_2\]

\(FCO_2\) in mol/day, \(A_{lake}\) = lake area in m2, \(\Delta CO_2\) in mol/m3 is the difference between water and air pCO2.

According to Vachon and Prairie (2013):

\[k_{600} = 2.51 + 1.48 \times U_{10} + 0.39 \times U_{10} \times log_{10} (A_{lake})\]

with \(k_600\) in \(cm/h\), \(A\) in km2 and \(U_{10}\) in m/s

\(k_{CO_2}\) has to be adjusted for temperature. Crusius and Wanninkhof (2003):

\[k_{600} = k_{CO_2}\times \left( \frac{600}{Sc_{CO_2}} \right) ^{-n}\]

The Schmidt \(Sc_{CO_2}\) number is calculated from Wanninkhof (2014).

6.2 Compute ECO2

norway$pCO2_pred <- predict(pco2.toc, newdata = norway)

norway$Sc <- with(norway, 1923.6-125.06*temp_c+4.3733*temp_c^2-0.086781*temp_c^3) #@wanningkhof

norway$n <- NA
for(i in 1:length(norway$n)){
  if(norway$nws_m.s[i] < 3.7 & is.na(norway$nws_m.s[i]) == F){
    norway$n[i] = 2/3
  }else if(norway$nws_m.s[i] > 3.7 & is.na(norway$nws_m.s[i]) == F){
    norway$n[i] = 1/2
  } else if(is.na(norway$nws_m.s[i]) == T){
    norway$n[i] = NA
  }
} # adjusted n from Vachon


norway$k600 <- with(norway, 2.51+1.48*nws_m.s+0.39*nws_m.s*log10(lake.area)) # lake.area already in km2, in cm/h
                    
norway$kCO2 <- with(norway, k600*(600/Sc)^(n))*24*1e-2 # from cm/h to m/day

norway$k600_low <- with(norway, 2.07+0.25*nws_m.s^1.7) # lake area in km2. Cole & Caraco 1998
                    
norway$kCO2_low <- with(norway, k600_low*(600/Sc)^(n))*24*1e-2

norway$ECO2 <- with(norway, kCO2*(fCO2-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day

norway$ECO2_low <- with(norway, kCO2_low*(fCO2-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day

norway$ECO2_toc <- with(norway, kCO2*(pCO2_pred-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day

norway$ECO2_toc_low <- with(norway, kCO2_low*(pCO2_pred-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day


norway$ECO2_ta <- with(norway, kCO2*(ta_fCO2-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day

norway$ECO2_ta_low <- with(norway, kCO2_low*(ta_fCO2-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day

nlss$Sc <- with(nlss, 1923.6-125.06*temp_c+4.3733*temp_c^2-0.086781*temp_c^3) #@wanningkhof

nlss$n <- NA
for(i in 1:length(nlss$n)){
  if(nlss$nws_m.s[i] < 3.7 & is.na(nlss$nws_m.s[i]) == F){
    nlss$n[i] = 2/3
  }else if(nlss$nws_m.s[i] > 3.7 & is.na(nlss$nws_m.s[i]) == F){
    nlss$n[i] = 1/2
  } else if(is.na(nlss$nws_m.s[i]) == T){
    nlss$n[i] = NA
  }
}


nlss$k600 <- with(nlss, 2.51+1.48*nws_m.s+0.39*nws_m.s*log10(lake.area)) # lake area in km2
                    
nlss$kCO2 <- with(nlss, k600*(600/Sc)^(n))*24*1e-2

nlss$k600_low <- with(nlss, 2.07+0.25*nws_m.s^1.7) # lake area in km2. Cole & Caraco 1998
nlss$kCO2_low <- with(nlss, k600_low*(600/Sc)^(n))*24*1e-2

nlss$ECO2_toc <- with(nlss, kCO2*(pCO2_toc-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day
nlss$ECO2_toc_low <- with(nlss, kCO2_low*(pCO2_toc-fCO2.atm)*K0*1e3 * 12.011)

nlss$ECO2_ta <- with(nlss, kCO2*(pCO2_ta-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day
nlss$ECO2_ta_low <- with(nlss, kCO2_low*(pCO2_ta-fCO2.atm)*K0*1e3 * 12.011) # in gC/m2/day

6.3 Compare ECO2 from TOC and ECO2 from TA

Comparison of the ECO2 obtained by calculation pCO2 from TOC or TA (in that case, we remove samples in which pH < 5.4).

no <- norway %>% 
  dplyr::select(c("survey", "fCO2" ,"pCO2_pred", "ECO2_toc", "ECO2_toc_low")) %>% 
  mutate(nation = "Norway") %>% 
  setNames(c("survey","measured_pCO2","pCO2_toc","ECO2_high","ECO2_low","nation"))  %>% 
  dplyr::select(c("survey","nation","measured_pCO2","pCO2_toc","ECO2_high","ECO2_low"))

fns <- nlss %>% as_data_frame() %>%
  dplyr::select(c("nation", "pCO2_toc", "ECO2_toc", "ECO2_toc_low")) %>% 
  mutate(fCO2 = NA, survey = "nls_1995") %>% 
  setNames(c("nation","pCO2_toc","ECO2_high", "ECO2_low","measured_pCO2","survey")) %>% 
  dplyr::select(c("survey","nation","measured_pCO2","pCO2_toc","ECO2_high","ECO2_low"))

summary_eco2 <- rbind(no,fns) %>% group_by(nation, survey) %>% summarize_all(median, na.rm = T) 
kable(summary_eco2, caption = "Median of all variables") %>% kable_styling()

Table 6.1: Median of all variables

nation	survey	measured_pCO2	pCO2_toc	ECO2_high	ECO2_low
Finland	nls_1995		0.0010466	0.6485093	0.3937047
Norway	CBA_2019	0.0011381	0.0015612	0.7760363	0.4467789
Norway	N112_2004	0.0006845	0.0006695	0.2298677	0.1219191
Norway	nls_1995		0.0005846	0.1133226	0.0663061
Sweden	nls_1995		0.0009850	0.5774552	0.3625001

no <- norway %>% 
  dplyr::select(c("survey", "pH", "fCO2", "ta_fCO2", "ECO2_ta", "ECO2_ta_low")) %>% 
  mutate(nation = "Norway") %>% 
  setNames(c("survey","pH","measured_pCO2","pCO2_ta","ECO2_high","ECO2_low","nation"))  %>%
  dplyr::select(c("survey","nation","pH","measured_pCO2","pCO2_ta","ECO2_high","ECO2_low"))

fns <- nlss %>% as_data_frame() %>%
  dplyr::select(c("nation", "pH","pCO2_ta","ECO2_ta", "ECO2_ta_low")) %>% 
  mutate(fCO2 = NA, survey = "nls_1995") %>% 
  setNames(c("nation","pH","pCO2_ta","ECO2_high", "ECO2_low","measured_pCO2","survey")) %>% 
  dplyr::select(c("survey","nation","pH","measured_pCO2","pCO2_ta","ECO2_high","ECO2_low"))

summary_eco2_ta <- rbind(no,fns) %>% filter(pH > 5.4) %>% group_by(nation, survey) %>% summarize_all(median, na.rm = T) 
kable(summary_eco2_ta, caption = "Median of all variables, pH > 5.4") %>% kable_styling()

(#tab:summary-eco2_ta)Median of all variables, pH > 5.4

nation	survey	pH	measured_pCO2	pCO2_ta	ECO2_high	ECO2_low
Finland	nls_1995	6.700		0.0013406	0.8801672	0.5303916
Norway	CBA_2019	6.775	0.0011381	0.0014529	0.7340419	0.3619518
Norway	N112_2004	6.070	0.0006381	0.0009285	0.3790531	0.1897891
Norway	nls_1995	6.540		0.0007590	0.1992923	0.1199373
Sweden	nls_1995	6.850		0.0011476	0.7451497	0.4701856

6.4 Summary table with median and mean, TOC

no <- norway %>% 
  dplyr::select(c("survey", "fCO2" , "ECO2", "ECO2_toc","ECO2_low", "ECO2_toc_low")) 

medyear <- function(x){median(x, na.rm = T) * 365} # to convert gC/m2/d in gC/m2/year
avyear <- function(x){mean(x, na.rm = T) * 365}

summary_eco2.1 <- no %>% group_by(survey) %>% summarize_all(medyear) %>% mutate(fCO2 = fCO2/365*1e6)

summary_eco2.2 <- no %>% group_by(survey) %>% summarize_all(avyear) %>% mutate(fCO2 = fCO2/365*1e6)

no2 <- rbind(summary_eco2.1, summary_eco2.2) %>% arrange(survey) %>% mutate(survey = c("median","mean","median","mean"))

fen <- nlss %>% dplyr::select(c("pCO2_toc","ECO2_toc","ECO2_toc_low")) %>% 
  mutate(ECO2 = NA, ECO2_low = NA, fCO2 = pCO2_toc/365*1e6, survey = NA) %>%
  dplyr::select(c("survey","fCO2", "ECO2", "ECO2_toc", "ECO2_low","ECO2_toc_low"))
fen$lake.id <- NULL

summary_fen.1 <- fen %>% group_by(survey) %>% summarize_all(medyear) %>% mutate(survey= "median")
summary_fen.2 <- fen %>% group_by(survey) %>% summarize_all(avyear) %>% mutate(survey= "mean")

tot <- rbind(no2, summary_fen.1) %>% rbind(summary_fen.2)

kable(tot, digits = 2, col.names = c(" ","pCO2, uatm", "ECO2 from DIC in gC/m2/day","ECO2 from TOC in gC/m2/day","ECO2 from DIC in gC/m2/day","ECO2 from TOC in gC/m2/day")) %>% 
  kable_styling %>% 
  group_rows(group_label= "CBA", start_row = 1, end_row = 2) %>%
  group_rows(group_label= "N112", start_row = 3, end_row = 4) %>% 
  group_rows(group_label= "NLS", start_row = 5, end_row = 6) %>% 
  add_header_above(c(" " = 2, "High estimates" = 2, "Low estimates" = 2)) 

		High estimates		Low estimates
	pCO2, uatm	ECO2 from DIC in gC/m2/day	ECO2 from TOC in gC/m2/day	ECO2 from DIC in gC/m2/day	ECO2 from TOC in gC/m2/day
CBA
median	1138.11	188.63	283.25	103.13	163.07
mean	1449.22	257.25	294.77	151.06	165.10
N112
median	684.50	80.27	83.90	46.72	44.50
mean	779.18	109.49	95.83	60.31	52.14
NLS
median	932.23		176.27		107.48
mean	1002.07		210.83		139.80

kable(tot, digits = 2, col.names = c(" ","pCO2, uatm", "ECO2 from DIC in gC/m2/year","ECO2 from TOC in gC/m2/year","ECO2 from DIC in gC/m2/year","ECO2 from TOC in gC/m2/year")) %>% 
  kable_styling() %>% 
  group_rows(group_label= "CBA", start_row = 1, end_row = 2) %>%
  group_rows(group_label= "N112", start_row = 3, end_row = 4) %>%
  group_rows(group_label= "NLS", start_row = 5, end_row = 6) %>% 
  add_header_above(c(" " = 2, "High estimates" = 2, "Low estimates" = 2)) %>%
  save_kable(file = "compare.eco2.measured.png",zoom = 5)

6.5 Compare total emissions calculated from bins, with total emissions calculated from median and mean

We also compare with the efflux calculated by Hastie et al. (2018) by class of area. The efflux is given in TgC/year. We convert it to gC/m2/year for each country.

options(knitr.kable.NA = '')

p0 <- median(nlss$pCO2_toc, na.rm = T)*1e6
A0 <- sum(nlss$ake.area)
k0 <- nlss$kCO2 %>% median(na.rm = T) 
k0_low <- nlss$kCO2_low %>% median(na.rm = T)
E0 <- median(nlss$ECO2_toc * 365, na.rm = T) # gC/m2/y
E0_low <- median(nlss$ECO2_toc_low * 365, na.rm = T) # gC/m2/y

F0_realsum <-  with(nlss, sum(ECO2_toc * 365 *lake.area*1e6/12.011 * 43.99 * 1e-12, na.rm = T)) #MtCO2/y
F0_sumfrommedian <- with(nlss, E0*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)

F0_low_realsum <-  with(nlss, sum(ECO2_toc_low * 365 *lake.area*1e6/12.011 * 43.99 * 1e-12, na.rm = T)) #MtCO2/y
F0_low_sumfrommedian <- with(nlss, E0_low*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)

# Lake size < 0.1 km2

p1 <- nlss %>% subset(lake.area < 0.1) %>% pull(pCO2_toc) %>% median()*1e6
A1 <- nlss %>% subset(lake.area < 0.1) %>% pull(lake.area) %>% sum()

k1 <- with(subset(nlss, lake.area < 0.1), median(kCO2, na.rm = T)) 
E1 <- with(subset(nlss, lake.area < 0.1), median(ECO2_toc*365, na.rm = T)) #gC/m2/y

F1_realsum <- with(subset(nlss, lake.area < 0.1), sum(ECO2_toc * 365 *lake.area*1e6/12.011 * 43.99 * 1e-12, na.rm = T)) #MtCO2/y
F1_sumfrombin <- with(subset(nlss, lake.area < 0.1), E1*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)

  
k1_low <- with(subset(nlss, lake.area < 0.1), median(kCO2_low, na.rm = T)) 
E1_low <- with(subset(nlss, lake.area < 0.1), median(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F1_low_realsum <- with(subset(nlss, lake.area < 0.1), sum(ECO2_toc_low * 365/12.011 * 43.99  * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F1_low_sumfrombin <- with(subset(nlss, lake.area < 0.1), E1_low*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)


W1 <- 38.17*1e12/(208008*1e6) # gC/m2/year in Weyhenmeyer
W1_sum <- with(subset(nlss, lake.area < 0.1), W1*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

# 0.1 < Lake size < 1 km2

p2 <- nlss %>% subset(lake.area < 1 & lake.area > 0.1) %>% pull(pCO2_toc) %>% median()*1e6
A2 <- nlss %>% subset(lake.area < 1 & lake.area > 0.1) %>% pull(lake.area) %>% sum()

k2 <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), median(kCO2, na.rm = T)) 
E2 <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), median(ECO2_toc*365, na.rm = T)) #gC/m2/y

F2_realsum <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), sum(ECO2_toc * 365/12.011 * 43.99 * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F2_sumfrombin <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), E2*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)


k2_low <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), median(kCO2_low, na.rm = T)) 
E2_low <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), median(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F2_low_realsum <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), sum(ECO2_toc_low * 365/12.011 * 43.99 * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F2_low_sumfrombin <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), E2_low*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)



W2 <- 52.36*1e12/(282434*1e6) # gC/m2/year in W
W2_sum <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), W2*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

# 1 < Lake size < 10 km2

p3 <- nlss %>% subset(lake.area > 1 & lake.area < 10) %>% pull(pCO2_toc) %>% median()*1e6
A3 <- nlss %>% subset(lake.area > 1 & lake.area < 10) %>% pull(lake.area) %>% sum()

k3 <- with(subset(nlss, lake.area > 1 & lake.area < 10), median(kCO2, na.rm = T)) 
E3 <- with(subset(nlss, lake.area > 1 & lake.area < 10), median(ECO2_toc*365, na.rm = T)) #gC/m2/y

F3_realsum <- with(subset(nlss, lake.area > 1 & lake.area < 10), sum(ECO2_toc * 365/12.011 * 43.99 * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F3_sumfrombin <- with(subset(nlss, lake.area > 1 & lake.area < 10), E3*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)


k3_low <- with(subset(nlss, lake.area > 1 & lake.area < 10), median(kCO2_low, na.rm = T)) 
E3_low <- with(subset(nlss, lake.area > 1 & lake.area < 10), median(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F3_low_realsum <- with(subset(nlss, lake.area > 1 & lake.area < 10), sum(ECO2_toc_low * 365/12.011 * 43.99  * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F3_low_sumfrombin <- with(subset(nlss, lake.area > 1 & lake.area < 10), E3_low*sum(lake.area*1e6)/12.011 * 43.99  * 1e-12)


W3 <- 22.80*1e12/(286624*1e6) # gC/m2/year in W
W3_sum <- with(subset(nlss, lake.area > 1 & lake.area < 10), W3*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

# 1 < Lake size < 10 km2

p4 <- nlss %>% subset(lake.area > 10) %>% pull(pCO2_toc) %>% median()*1e6
A4 <- nlss %>% subset(lake.area > 10) %>% pull(lake.area) %>% sum()

k600_4 <- with(subset(nlss, lake.area > 10), median(k600*24*1e-2, na.rm = T))
k600_4_low <- with(subset(nlss, lake.area > 10), median(k600_low*24*1e-2, na.rm = T))

k4 <- with(subset(nlss, lake.area > 10), median(kCO2, na.rm = T)) 
E4 <- with(subset(nlss, lake.area > 10), median(ECO2_toc*365, na.rm = T)) #gC/m2/y

F4_realsum <- with(subset(nlss, lake.area > 10), sum(ECO2_toc* 365*lake.area*1e6/12.011 * 43.99  * 1e-12, na.rm = T)) #MtCO2/y
F4_sumfrombin <- with(subset(nlss, lake.area > 10), E4*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)



k4_low <- with(subset(nlss, lake.area > 10), median(kCO2_low, na.rm = T)) 
E4_low <- with(subset(nlss, lake.area > 10), median(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F4_low_realsum <- with(subset(nlss, lake.area > 10), sum(ECO2_toc_low* 365*lake.area*1e6/12.011 * 43.99  * 1e-12, na.rm = T)) #MtCO2/y
F4_low_sumfrombin <- with(subset(nlss, lake.area > 10), E4_low*sum(lake.area*1e6)/12.011 * 43.99  * 1e-12)


W4 <- 53.96*1e12/(570583*1e6) # gC/m2/year in W
W4_sum <- with(subset(nlss, lake.area > 10), W4*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

bin_FCO2 <- data.frame(lake.size = c("A < 0.1","0.1 < A < 1","1 < A < 10","> 10","sum"," "), 
          lake.area = c(A1, A2, A3, A4, NA,A0),
           pCO2 = c(p1,p2,p3,p4,NA,p0), 
           kCO2_low = c(k1_low,k2_low,k3_low,k4_low,NA,k0_low), 
           E_low = c(E1_low,E2_low,E3_low,E4_low,NA,E0_low),
           FCO2_low_bin = c(F1_low_sumfrombin, F2_low_sumfrombin, F3_low_sumfrombin, F4_low_sumfrombin, sum(F1_low_sumfrombin, F2_low_sumfrombin, F3_low_sumfrombin, F4_low_sumfrombin),F0_low_sumfrommedian),
            FCO2_low = c(F1_low_realsum, F2_low_realsum, F3_low_realsum, F4_low_realsum,sum(F1_low_realsum,F2_low_realsum,F3_low_realsum,F4_low_realsum),F0_low_realsum),
           kCO2_high = c(k1,k2,k3,k4, NA,K0),
           E_high = c(E1,E2,E3,E4, NA,E0),
           FCO2_high_bin = c(F1_sumfrombin, F2_sumfrombin, F3_sumfrombin, F4_sumfrombin, sum(F1_sumfrombin, F2_sumfrombin, F3_sumfrombin, F4_sumfrombin),F0_sumfrommedian),
          FCO2_high = c(F1_realsum, F2_realsum, F3_realsum, F4_realsum, sum(F1_realsum, F2_realsum, F3_realsum, F4_realsum),F0_realsum),
           Wey = c(W1,W2,W3,W4, NA,NA),
           Wey_sum = c(W1_sum, W2_sum, W3_sum, W4_sum, sum(W1_sum, W2_sum, W3_sum, W4_sum),NA))


kable(bin_FCO2, digits = 2, col.names = c("A = lake area in km2","Total lake area in km2","median pCO2, uatm","median kCO2, m2/d","median ECO2, g/m2/y", "binned FCO2, MtCO2/y","actual FCO2, MtCO2/y","kCO2, m2/d","median ECO2, g/m2/y", "binned FCO2, MtCO2/y", "actual FCO2, MtCO2/y","median ECO2, g/m2/day", "FCO2, MtCO2/y"),
      caption = "Norway, Sweden, Finland, median value") %>% kable_styling() %>% 
  add_header_above(c("Lake class" = 2, " " = 1, "Low estimate" = 4, "High estimate" = 4, "Hastie et al." = 2)) %>%
  group_rows(group_label= "All lakes", start_row = 6, end_row = 6) %>%
  column_spec(column = c(5,6,9,10,12), bold = T)

(#tab:summary_bin_toc_median)Norway, Sweden, Finland, median value

Lake class			Low estimate				High estimate				Hastie et al.
A = lake area in km2	Total lake area in km2	median pCO2, uatm	median kCO2, m2/d	median ECO2, g/m2/y	binned FCO2, MtCO2/y	actual FCO2, MtCO2/y	kCO2, m2/d	median ECO2, g/m2/y	binned FCO2, MtCO2/y	actual FCO2, MtCO2/y	median ECO2, g/m2/day	FCO2, MtCO2/y
A < 0.1	89.23	949.84	0.55	92.35	0.03	0.05	0.78	131.92	0.04	0.06	183.50	0.06
0.1 < A < 1	449.17	958.64	0.73	120.60	0.20	0.24	1.14	189.21	0.31	0.37	185.39	0.30
1 < A < 10	2386.51	914.63	0.78	114.53	1.00	1.14	1.44	214.93	1.88	2.11	79.55	0.70
> 10	32393.63	875.03	0.66	99.18	11.77	14.15	1.57	235.73	27.97	36.79	94.57	11.22
sum					13.00	15.57			30.20	39.33		12.28
All lakes
	0.00	932.23	0.64	107.48	13.90	15.57	0.07	176.27	22.80	39.33

p0 <- mean(nlss$pCO2_toc, na.rm = T)*1e6
A0 <- sum(nlss$ake.area)
k0 <- nlss$kCO2 %>% mean(na.rm = T) 
k0_low <- nlss$kCO2_low %>% mean(na.rm = T)
E0 <- mean(nlss$ECO2_toc * 365, na.rm = T) # gC/m2/y
E0_low <- mean(nlss$ECO2_toc_low * 365, na.rm = T) # gC/m2/y

F0_realsum <-  with(nlss, sum(ECO2_toc * 365 *lake.area*1e6/12.011 * 43.99 * 1e-12, na.rm = T)) #MtCO2/y
F0_sumfrommean <- with(nlss, E0*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)

F0_low_realsum <-  with(nlss, sum(ECO2_toc_low * 365 *lake.area*1e6/12.011 * 43.99 * 1e-12, na.rm = T)) #MtCO2/y
F0_low_sumfrommean <- with(nlss, E0_low*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)

# Lake size < 0.1 km2

p1 <- nlss %>% subset(lake.area < 0.1) %>% pull(pCO2_toc) %>% mean()*1e6
A1 <- nlss %>% subset(lake.area < 0.1) %>% pull(lake.area) %>% sum()

k1 <- with(subset(nlss, lake.area < 0.1), mean(kCO2, na.rm = T)) 
E1 <- with(subset(nlss, lake.area < 0.1), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y

F1_realsum <- with(subset(nlss, lake.area < 0.1), sum(ECO2_toc * 365 *lake.area*1e6/12.011 * 43.99 * 1e-12, na.rm = T)) #MtCO2/y
F1_sumfrombin <- with(subset(nlss, lake.area < 0.1), E1*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)

  
k1_low <- with(subset(nlss, lake.area < 0.1), mean(kCO2_low, na.rm = T)) 
E1_low <- with(subset(nlss, lake.area < 0.1), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F1_low_realsum <- with(subset(nlss, lake.area < 0.1), sum(ECO2_toc_low * 365/12.011 * 43.99  * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F1_low_sumfrombin <- with(subset(nlss, lake.area < 0.1), E1_low*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)


W1 <- 38.17*1e12/(208008*1e6) # gC/m2/year in Weyhenmeyer
W1_sum <- with(subset(nlss, lake.area < 0.1), W1*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

# 0.1 < Lake size < 1 km2

p2 <- nlss %>% subset(lake.area < 1 & lake.area > 0.1) %>% pull(pCO2_toc) %>% mean()*1e6

k2 <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), mean(kCO2, na.rm = T)) 
E2 <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y

F2_realsum <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), sum(ECO2_toc * 365/12.011 * 43.99 * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F2_sumfrombin <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), E2*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)


k2_low <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), mean(kCO2_low, na.rm = T)) 
E2_low <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F2_low_realsum <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), sum(ECO2_toc_low * 365/12.011 * 43.99 * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F2_low_sumfrombin <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), E2_low*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)



W2 <- 52.36*1e12/(282434*1e6) # gC/m2/year in W
W2_sum <- with(subset(nlss, lake.area < 1 & lake.area > 0.1), W2*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

# 1 < Lake size < 10 km2

p3 <- nlss %>% subset(lake.area > 1 & lake.area < 10) %>% pull(pCO2_toc) %>% mean()*1e6

k3 <- with(subset(nlss, lake.area > 1 & lake.area < 10), mean(kCO2, na.rm = T)) 
E3 <- with(subset(nlss, lake.area > 1 & lake.area < 10), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y

F3_realsum <- with(subset(nlss, lake.area > 1 & lake.area < 10), sum(ECO2_toc * 365/12.011 * 43.99 * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F3_sumfrombin <- with(subset(nlss, lake.area > 1 & lake.area < 10), E3*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)


k3_low <- with(subset(nlss, lake.area > 1 & lake.area < 10), mean(kCO2_low, na.rm = T)) 
E3_low <- with(subset(nlss, lake.area > 1 & lake.area < 10), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F3_low_realsum <- with(subset(nlss, lake.area > 1 & lake.area < 10), sum(ECO2_toc_low * 365/12.011 * 43.99  * 1e-12*lake.area*1e6, na.rm = T)) #MtCO2/y
F3_low_sumfrombin <- with(subset(nlss, lake.area > 1 & lake.area < 10), E3_low*sum(lake.area*1e6)/12.011 * 43.99  * 1e-12)


W3 <- 22.80*1e12/(286624*1e6) # gC/m2/year in W
W3_sum <- with(subset(nlss, lake.area > 1 & lake.area < 10), W3*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

# 1 < Lake size < 10 km2

p4 <- nlss %>% subset(lake.area > 10) %>% pull(pCO2_toc) %>% mean()*1e6

k600_4 <- with(subset(nlss, lake.area > 10), mean(k600*24*1e-2, na.rm = T))
k600_4_low <- with(subset(nlss, lake.area > 10), mean(k600_low*24*1e-2, na.rm = T))

k4 <- with(subset(nlss, lake.area > 10), mean(kCO2, na.rm = T)) 
E4 <- with(subset(nlss, lake.area > 10), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y

F4_realsum <- with(subset(nlss, lake.area > 10), sum(ECO2_toc* 365*lake.area*1e6/12.011 * 43.99  * 1e-12, na.rm = T)) #MtCO2/y
F4_sumfrombin <- with(subset(nlss, lake.area > 10), E4*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12)



k4_low <- with(subset(nlss, lake.area > 10), mean(kCO2_low, na.rm = T)) 
E4_low <- with(subset(nlss, lake.area > 10), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y

F4_low_realsum <- with(subset(nlss, lake.area > 10), sum(ECO2_toc_low* 365*lake.area*1e6/12.011 * 43.99  * 1e-12, na.rm = T)) #MtCO2/y
F4_low_sumfrombin <- with(subset(nlss, lake.area > 10), E4_low*sum(lake.area*1e6)/12.011 * 43.99  * 1e-12)


W4 <- 53.96*1e12/(570583*1e6) # gC/m2/year in W
W4_sum <- with(subset(nlss, lake.area > 10), W4*sum(lake.area*1e6)/12.011 * 43.99 * 1e-12) # MtCO2/y

bin_FCO2 <- data.frame(lake.size = c("A < 0.1","0.1 < A < 1","1 < A < 10","> 10","sum"," "), 
           pCO2 = c(p1,p2,p3,p4,NA,p0), 
           kCO2_low = c(k1_low,k2_low,k3_low,k4_low,NA,k0_low), 
           E_low = c(E1_low,E2_low,E3_low,E4_low,NA,E0_low),
           FCO2_low_bin = c(F1_low_sumfrombin, F2_low_sumfrombin, F3_low_sumfrombin, F4_low_sumfrombin, sum(F1_low_sumfrombin, F2_low_sumfrombin, F3_low_sumfrombin, F4_low_sumfrombin),F0_low_sumfrommean),
            FCO2_low = c(F1_low_realsum, F2_low_realsum, F3_low_realsum, F4_low_realsum,sum(F1_low_realsum,F2_low_realsum,F3_low_realsum,F4_low_realsum),F0_low_realsum),
           kCO2_high = c(k1,k2,k3,k4, NA,K0),
           E_high = c(E1,E2,E3,E4, NA,E0),
           FCO2_high_bin = c(F1_sumfrombin, F2_sumfrombin, F3_sumfrombin, F4_sumfrombin, sum(F1_sumfrombin, F2_sumfrombin, F3_sumfrombin, F4_sumfrombin),F0_sumfrommean),
          FCO2_high = c(F1_realsum, F2_realsum, F3_realsum, F4_realsum, sum(F1_realsum, F2_realsum, F3_realsum, F4_realsum),F0_realsum),
           Wey = c(W1,W2,W3,W4, NA,NA),
           Wey_sum = c(W1_sum, W2_sum, W3_sum, W4_sum, sum(W1_sum, W2_sum, W3_sum, W4_sum),NA))


kable(bin_FCO2, digits = 2, col.names = c("A = lake area in km2","mean pCO2, uatm","mean kCO2, m2/d","mean ECO2, g/m2/y", "binned FCO2, MtCO2/y","actual FCO2, MtCO2/y","kCO2, m2/d","mean ECO2, g/m2/y", "binned FCO2, MtCO2/y", "actual FCO2, MtCO2/y","mean ECO2, g/m2/day", "FCO2, MtCO2/y"),
      caption = "Norway, Sweden, Finland; mean value") %>% kable_styling() %>% 
  add_header_above(c("Lake class" = 1, " " = 1, "Low estimate" = 4, "High estimate" = 4, "Hastie et al." = 2)) %>%
  group_rows(group_label= "All lakes", start_row = 6, end_row = 6) %>%
  column_spec(column = c(5,6,9,10,12), bold = T)

(#tab:summary_bin_toc_mean)Norway, Sweden, Finland; mean value

Lake class		Low estimate				High estimate				Hastie et al.
A = lake area in km2	mean pCO2, uatm	mean kCO2, m2/d	mean ECO2, g/m2/y	binned FCO2, MtCO2/y	actual FCO2, MtCO2/y	kCO2, m2/d	mean ECO2, g/m2/y	binned FCO2, MtCO2/y	actual FCO2, MtCO2/y	mean ECO2, g/m2/day	FCO2, MtCO2/y
A < 0.1	1038.31	0.64	142.96	0.05	0.05	0.85	184.62	0.06	0.06	183.50	0.06
0.1 < A < 1	1022.91	0.71	147.52	0.24	0.24	1.10	221.85	0.36	0.37	185.39	0.30
1 < A < 10	942.25	0.74	131.51	1.15	1.14	1.35	236.13	2.06	2.11	79.55	0.70
> 10	862.77	0.73	107.18	12.72	14.15	1.63	236.16	28.02	36.79	94.57	11.22
sum				14.15	15.57			30.51	39.33		12.28
All lakes
	1002.07	0.69	139.80	18.08	15.57	0.07	210.83	27.27	39.33

6.6 Bin estimation by country

nor <- filter(nlss, nation == "Norway")
inland.waters <- 20221 * 1e6 # km2 to m2, @SSB

p0 <- mean(nor$pCO2_toc, na.rm = T)*1e6
k0 <- mean(nor$kCO2, na.rm = T)
E0 <- mean(nor$ECO2_toc, na.rm = T)*365 # in gC/m2/year
F0 <- E0*inland.waters/12.011 * 43.99 * 1e-12 #MtCO2/t

k0_low <- mean(nor$kCO2_low, na.rm = T)
E0_low <- mean(nor$ECO2_toc_low, na.rm = T) *365 # in gC/m2/year
F0_low <- E0_low*inland.waters/12.011 * 43.99 * 1e-12 #MtCO2/t


A0 <- sum(subset(nor, lake.area < 100)$lake.area) # exclude big lakes

# Lake size < 0.1 km2

p1 <- nor %>% subset(lake.area < 0.1) %>% pull(pCO2_toc) %>% mean()*1e6
A1 <- nor %>% subset(lake.area < 0.1) %>% pull(lake.area) %>% sum()
A1_inland <- A1/A0*inland.waters

k1 <- with(subset(nor, lake.area < 0.1), mean(kCO2, na.rm = T)) 
E1 <- with(subset(nor, lake.area < 0.1), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y
F1 <- E1*A1_inland/12.011 * 43.99 * 1e-12 #MtCO2/t

  
k1_low <- with(subset(nor, lake.area < 0.1), mean(kCO2_low, na.rm = T)) 
E1_low <- with(subset(nor, lake.area < 0.1), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F1_low <- E1_low*A1_inland/12.011 * 43.99 * 1e-12

# 0.1 < Lake size < 1 km2

p2 <- nor %>% subset(lake.area < 1 & lake.area > 0.1) %>% pull(pCO2_toc) %>% mean()*1e6
A2 <- nor %>% subset(lake.area < 1 & lake.area > 0.1) %>% pull(lake.area) %>% sum()
A2_inland <- A2/A0*inland.waters

k2 <- with(subset(nor, lake.area < 1 & lake.area > 0.1), mean(kCO2, na.rm = T)) 
E2 <- with(subset(nor, lake.area < 1 & lake.area > 0.1), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y
F2 <- E2*A2_inland/12.011 * 43.99 * 1e-12


k2_low <- with(subset(nor, lake.area < 1 & lake.area > 0.1), mean(kCO2_low, na.rm = T)) 
E2_low <- with(subset(nor, lake.area < 1 & lake.area > 0.1), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F2_low <- E2_low*A2_inland/12.011 * 43.99 * 1e-12

# 1 < Lake size < 10 km2

p3 <- nor %>% subset(lake.area > 1 & lake.area < 10) %>% pull(pCO2_toc) %>% mean()*1e6
A3 <- nor %>% subset(lake.area > 1 & lake.area < 10) %>% pull(lake.area) %>% sum()
A3_inland <- A3/A0*inland.waters

k3 <- with(subset(nor, lake.area > 1 & lake.area < 10), mean(kCO2, na.rm = T)) 
E3 <- with(subset(nor, lake.area > 1 & lake.area < 10), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y

F3 <- E3*A3_inland/12.011 * 43.99 * 1e-12


k3_low <- with(subset(nor, lake.area > 1 & lake.area < 10), mean(kCO2_low, na.rm = T)) 
E3_low <- with(subset(nor, lake.area > 1 & lake.area < 10), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F3_low <- E3_low*A3_inland/12.011 * 43.99  * 1e-12

# 1 < Lake size < 10 km2

p4 <- nor %>% subset(lake.area > 10 & lake.area < 100) %>% pull(pCO2_toc) %>% mean()*1e6
A4 <- nor %>% subset(lake.area > 10 & lake.area < 100) %>% pull(lake.area) %>% sum()
A4_inland <- A4/A0*inland.waters

k4 <- with(subset(nor, lake.area > 10 & lake.area < 100), mean(kCO2, na.rm = T)) 
E4 <- with(subset(nor, lake.area > 10 & lake.area < 100), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y
F4 <- E4*A4_inland/12.011 * 43.99 * 1e-12

k4_low <- with(subset(nor, lake.area > 10 & lake.area < 100), mean(kCO2_low, na.rm = T)) 
E4_low <- with(subset(nor, lake.area > 10 & lake.area < 100), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F4_low <- E4_low*A4_inland/12.011 * 43.99  * 1e-12

# Big lakes
p5 <- nor %>% subset(lake.area > 100) %>% pull(pCO2_toc) %>% mean()*1e6
A5 <- nor %>% subset(lake.area > 100) %>% pull(lake.area) %>% sum()*1e6 # km2 to m2

k5 <- with(subset(nor, lake.area > 100), mean(kCO2, na.rm = T)) 
E5 <- with(subset(nor, lake.area > 100), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y
F5 <- E5*A5/12.011 * 43.99 * 1e-12
F

## [1] FALSE

k5_low <- with(subset(nor, lake.area > 100), mean(kCO2_low, na.rm = T)) 
E5_low <- with(subset(nor, lake.area > 100), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F5_low <- E5_low*A5/12.011 * 43.99  * 1e-12


bin_FCO2 <- data.frame(
            lake.size = c("A < 0.1","0.1 < A < 1","1 < A < 10","> 10", "Big lakes (> 100)","Total","All lakes"),
           pCO2 = c(p1,p2,p3,p4,p5,NA,p0), 
           kCO2_low = c(k1_low,k2_low,k3_low,k4_low, k5_low,NA,k0_low), 
           E_low = c(E1_low,E2_low,E3_low,E4_low,E5_low,NA, E0_low),
           FCO2_low = c(F1_low, F2_low, F3_low, F4_low, F5_low, sum(F1_low, F2_low, F3_low, F4_low, F5_low), F0_low),
           kCO2_high = c(k1,k2,k3,k4,k5, NA,k0),
           E_high = c(E1,E2,E3,E4, E5,NA, E0),
           FCO2_high = c(F1, F2, F3, F4, F5, sum(F1, F2, F3, F4, F5),F0))


kable(bin_FCO2, digits = 2, col.names = c("A = lake area in km2","mean pCO2, uatm","mean kCO2, m2/d","mean ECO2, g/m2/y", "binned FCO2, MtCO2/y","kCO2, m2/d","mean ECO2, g/m2/y", "binned FCO2, MtCO2/y"), caption = "Norway") %>% kable_styling() %>% 
  add_header_above(c("Lake class" = 1, " " = 1, "Low estimate" = 3, "High estimate" = 3)) %>%
  group_rows(group_label = "All lakes", start_row = 7, end_row = 7)

Table 6.2: Norway

Lake class		Low estimate			High estimate
A = lake area in km2	mean pCO2, uatm	mean kCO2, m2/d	mean ECO2, g/m2/y	binned FCO2, MtCO2/y	kCO2, m2/d	mean ECO2, g/m2/y	binned FCO2, MtCO2/y
A < 0.1	697.97	0.41	43.37	0.06	0.61	64.69	0.09
0.1 < A < 1	661.21	0.42	38.61	0.21	0.70	63.95	0.35
1 < A < 10	593.47	0.36	30.01	0.72	0.70	57.40	1.38
> 10	552.17	0.34	25.97	1.12	0.74	56.45	2.44
Big lakes (> 100)	563.30	0.31	20.85	0.08	0.71	47.80	0.19
Total				2.19			4.44
All lakes
All lakes	658.49	0.40	38.31	2.84	0.67	62.60	4.64

swe <- filter(nlss, nation == "Sweden")
boxplot(swe$lake.area)

inland.waters <- 4014169.92 * 1e4 # ha to m2, @SCB

p0 <- mean(swe$pCO2_toc, na.rm = T)*1e6
k0 <- mean(swe$kCO2, na.rm = T)
E0 <- mean(swe$ECO2_toc, na.rm = T)*365 # in gC/m2/year
F0 <- E0*inland.waters/12.011 * 43.99 * 1e-12 #MtCO2/t

k0_low <- mean(swe$kCO2_low, na.rm = T)
E0_low <- mean(swe$ECO2_toc_low, na.rm = T) *365 # in gC/m2/year
F0_low <- E0_low*inland.waters/12.011 * 43.99 * 1e-12 #MtCO2/t


A0 <- sum(subset(swe, lake.area < 100)$lake.area) # exclude big lakes

# Lake size < 0.1 km2

p1 <- swe %>% subset(lake.area < 0.1) %>% pull(pCO2_toc) %>% mean()*1e6
A1 <- swe %>% subset(lake.area < 0.1) %>% pull(lake.area) %>% sum()
A1_inland <- A1/A0*inland.waters

k1 <- with(subset(swe, lake.area < 0.1), mean(kCO2, na.rm = T)) 
E1 <- with(subset(swe, lake.area < 0.1), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y
F1 <- E1*A1_inland/12.011 * 43.99 * 1e-12 #MtCO2/t

  
k1_low <- with(subset(swe, lake.area < 0.1), mean(kCO2_low, na.rm = T)) 
E1_low <- with(subset(swe, lake.area < 0.1), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F1_low <- E1_low*A1_inland/12.011 * 43.99 * 1e-12

# 0.1 < Lake size < 1 km2

p2 <- swe %>% subset(lake.area < 1 & lake.area > 0.1) %>% pull(pCO2_toc) %>% mean()*1e6
A2 <- swe %>% subset(lake.area < 1 & lake.area > 0.1) %>% pull(lake.area) %>% sum()
A2_inland <- A2/A0*inland.waters

k2 <- with(subset(swe, lake.area < 1 & lake.area > 0.1), mean(kCO2, na.rm = T)) 
E2 <- with(subset(swe, lake.area < 1 & lake.area > 0.1), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y
F2 <- E2*A2_inland/12.011 * 43.99 * 1e-12


k2_low <- with(subset(swe, lake.area < 1 & lake.area > 0.1), mean(kCO2_low, na.rm = T)) 
E2_low <- with(subset(swe, lake.area < 1 & lake.area > 0.1), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F2_low <- E2_low*A2_inland/12.011 * 43.99 * 1e-12

# 1 < Lake size < 10 km2

p3 <- swe %>% subset(lake.area > 1 & lake.area < 10) %>% pull(pCO2_toc) %>% mean()*1e6
A3 <- swe %>% subset(lake.area > 1 & lake.area < 10) %>% pull(lake.area) %>% sum()
A3_inland <- A3/A0*inland.waters

k3 <- with(subset(swe, lake.area > 1 & lake.area < 10), mean(kCO2, na.rm = T)) 
E3 <- with(subset(swe, lake.area > 1 & lake.area < 10), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y

F3 <- E3*A3_inland/12.011 * 43.99 * 1e-12


k3_low <- with(subset(swe, lake.area > 1 & lake.area < 10), mean(kCO2_low, na.rm = T)) 
E3_low <- with(subset(swe, lake.area > 1 & lake.area < 10), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F3_low <- E3_low*A3_inland/12.011 * 43.99  * 1e-12

# 1 < Lake size < 10 km2

p4 <- swe %>% subset(lake.area > 10 & lake.area < 100) %>% pull(pCO2_toc) %>% mean()*1e6
A4 <- swe %>% subset(lake.area > 10 & lake.area < 100) %>% pull(lake.area) %>% sum()
A4_inland <- A4/A0*inland.waters

k4 <- with(subset(swe, lake.area > 10 & lake.area < 100), mean(kCO2, na.rm = T)) 
E4 <- with(subset(swe, lake.area > 10 & lake.area < 100), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y
F4 <- E4*A4_inland/12.011 * 43.99 * 1e-12

k4_low <- with(subset(swe, lake.area > 10 & lake.area < 100), mean(kCO2_low, na.rm = T)) 
E4_low <- with(subset(swe, lake.area > 10 & lake.area < 100), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F4_low <- E4_low*A4_inland/12.011 * 43.99  * 1e-12

# Big lakes
p5 <- swe %>% subset(lake.area > 100) %>% pull(pCO2_toc) %>% mean()*1e6
A5 <- swe %>% subset(lake.area > 100) %>% pull(lake.area) %>% sum()*1e6 # km2 to m2

k5 <- with(subset(swe, lake.area > 100), mean(kCO2, na.rm = T)) 
E5 <- with(subset(swe, lake.area > 100), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y
F5 <- E5*A5/12.011 * 43.99 * 1e-12
F

## [1] FALSE

k5_low <- with(subset(swe, lake.area > 100), mean(kCO2_low, na.rm = T)) 
E5_low <- with(subset(swe, lake.area > 100), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F5_low <- E5_low*A5/12.011 * 43.99  * 1e-12


bin_FCO2 <- data.frame(
            lake.size = c("A < 0.1","0.1 < A < 1","1 < A < 10","> 10", "Big lakes (> 100)","Total","All lakes"),
           pCO2 = c(p1,p2,p3,p4,p5,NA,p0), 
           kCO2_low = c(k1_low,k2_low,k3_low,k4_low, k5_low,NA,k0_low), 
           E_low = c(E1_low,E2_low,E3_low,E4_low,E5_low,NA, E0_low),
           FCO2_low = c(F1_low, F2_low, F3_low, F4_low, F5_low, sum(F1_low, F2_low, F3_low, F4_low, F5_low), F0_low),
           kCO2_high = c(k1,k2,k3,k4,k5, NA,k0),
           E_high = c(E1,E2,E3,E4, E5,NA, E0),
           FCO2_high = c(F1, F2, F3, F4, F5, sum(F1, F2, F3, F4, F5),F0))


kable(bin_FCO2, digits = 2, col.names = c("A = lake area in km2","mean pCO2, uatm","mean kCO2, m2/d","mean ECO2, g/m2/y", "binned FCO2, MtCO2/y","kCO2, m2/d","mean ECO2, g/m2/y", "binned FCO2, MtCO2/y"), caption = "Sweden") %>% kable_styling() %>% 
  add_header_above(c("Lake class" = 1, " " = 1, "Low estimate" = 3, "High estimate" = 3)) %>%
  group_rows(group_label = "All lakes", start_row = 7, end_row = 7)

Table 6.3: Sweden

Lake class		Low estimate			High estimate
A = lake area in km2	mean pCO2, uatm	mean kCO2, m2/d	mean ECO2, g/m2/y	binned FCO2, MtCO2/y	kCO2, m2/d	mean ECO2, g/m2/y	binned FCO2, MtCO2/y
A < 0.1	1083.64	0.68	162.21	0.28	0.90	206.53	0.36
0.1 < A < 1	1106.08	0.81	182.15	1.70	1.24	270.88	2.53
1 < A < 10	995.81	0.84	155.49	7.59	1.52	277.56	13.56
> 10	835.07	0.80	113.79	9.91	1.69	238.09	20.74
Big lakes (> 100)	723.08	0.73	82.33	3.52	1.85	207.91	8.89
Total				23.01			46.08
All lakes
All lakes	1058.45	0.76	164.29	24.15	1.18	243.11	35.74

fin <- filter(nlss, nation == "Finland")
boxplot(fin$lake.area)

inland.waters <- 34515 * 1e6 # km2 to m2, @Statfi

p0 <- mean(fin$pCO2_toc, na.rm = T)*1e6
k0 <- mean(fin$kCO2, na.rm = T)
E0 <- mean(fin$ECO2_toc, na.rm = T)*365 # in gC/m2/year
F0 <- E0*inland.waters/12.011 * 43.99 * 1e-12 #MtCO2/t

k0_low <- mean(fin$kCO2_low, na.rm = T)
E0_low <- mean(fin$ECO2_toc_low, na.rm = T) *365 # in gC/m2/year
F0_low <- E0_low*inland.waters/12.011 * 43.99 * 1e-12 #MtCO2/t


A0 <- sum(subset(fin, lake.area < 100)$lake.area) # exclude big lakes

# Lake size < 0.1 km2

p1 <- fin %>% subset(lake.area < 0.1) %>% pull(pCO2_toc) %>% mean()*1e6
A1 <- fin %>% subset(lake.area < 0.1) %>% pull(lake.area) %>% sum()
A1_inland <- A1/A0*inland.waters

k1 <- with(subset(fin, lake.area < 0.1), mean(kCO2, na.rm = T)) 
E1 <- with(subset(fin, lake.area < 0.1), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y
F1 <- E1*A1_inland/12.011 * 43.99 * 1e-12 #MtCO2/t

  
k1_low <- with(subset(fin, lake.area < 0.1), mean(kCO2_low, na.rm = T)) 
E1_low <- with(subset(fin, lake.area < 0.1), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F1_low <- E1_low*A1_inland/12.011 * 43.99 * 1e-12

# 0.1 < Lake size < 1 km2

p2 <- fin %>% subset(lake.area < 1 & lake.area > 0.1) %>% pull(pCO2_toc) %>% mean()*1e6
A2 <- fin %>% subset(lake.area < 1 & lake.area > 0.1) %>% pull(lake.area) %>% sum()
A2_inland <- A2/A0*inland.waters

k2 <- with(subset(fin, lake.area < 1 & lake.area > 0.1), mean(kCO2, na.rm = T)) 
E2 <- with(subset(fin, lake.area < 1 & lake.area > 0.1), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y
F2 <- E2*A2_inland/12.011 * 43.99 * 1e-12


k2_low <- with(subset(fin, lake.area < 1 & lake.area > 0.1), mean(kCO2_low, na.rm = T)) 
E2_low <- with(subset(fin, lake.area < 1 & lake.area > 0.1), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F2_low <- E2_low*A2_inland/12.011 * 43.99 * 1e-12

# 1 < Lake size < 10 km2

p3 <- fin %>% subset(lake.area > 1 & lake.area < 10) %>% pull(pCO2_toc) %>% mean()*1e6
A3 <- fin %>% subset(lake.area > 1 & lake.area < 10) %>% pull(lake.area) %>% sum()
A3_inland <- A3/A0*inland.waters

k3 <- with(subset(fin, lake.area > 1 & lake.area < 10), mean(kCO2, na.rm = T)) 
E3 <- with(subset(fin, lake.area > 1 & lake.area < 10), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y

F3 <- E3*A3_inland/12.011 * 43.99 * 1e-12


k3_low <- with(subset(fin, lake.area > 1 & lake.area < 10), mean(kCO2_low, na.rm = T)) 
E3_low <- with(subset(fin, lake.area > 1 & lake.area < 10), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F3_low <- E3_low*A3_inland/12.011 * 43.99  * 1e-12

# 1 < Lake size < 10 km2

p4 <- fin %>% subset(lake.area > 10 & lake.area < 100) %>% pull(pCO2_toc) %>% mean()*1e6
A4 <- fin %>% subset(lake.area > 10 & lake.area < 100) %>% pull(lake.area) %>% sum()
A4_inland <- A4/A0*inland.waters

k4 <- with(subset(fin, lake.area > 10 & lake.area < 100), mean(kCO2, na.rm = T)) 
E4 <- with(subset(fin, lake.area > 10 & lake.area < 100), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y
F4 <- E4*A4_inland/12.011 * 43.99 * 1e-12

k4_low <- with(subset(fin, lake.area > 10 & lake.area < 100), mean(kCO2_low, na.rm = T)) 
E4_low <- with(subset(fin, lake.area > 10 & lake.area < 100), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F4_low <- E4_low*A4_inland/12.011 * 43.99  * 1e-12

# Big lakes
p5 <- fin %>% subset(lake.area > 100) %>% pull(pCO2_toc) %>% mean()*1e6
A5 <- fin %>% subset(lake.area > 100) %>% pull(lake.area) %>% sum()*1e6 # km2 to m2

k5 <- with(subset(fin, lake.area > 100), mean(kCO2, na.rm = T)) 
E5 <- with(subset(fin, lake.area > 100), mean(ECO2_toc*365, na.rm = T)) #gC/m2/y
F5 <- E5*A5/12.011 * 43.99 * 1e-12
F

## [1] FALSE

k5_low <- with(subset(fin, lake.area > 100), mean(kCO2_low, na.rm = T)) 
E5_low <- with(subset(fin, lake.area > 100), mean(ECO2_toc_low*365, na.rm = T)) #gC/m2/y
F5_low <- E5_low*A5/12.011 * 43.99  * 1e-12


bin_FCO2 <- data.frame(
            lake.size = c("A < 0.1","0.1 < A < 1","1 < A < 10","> 10", "Big lakes (> 100)","Total","All lakes"),
           pCO2 = c(p1,p2,p3,p4,p5,NA,p0), 
           kCO2_low = c(k1_low,k2_low,k3_low,k4_low, k5_low,NA,k0_low), 
           E_low = c(E1_low,E2_low,E3_low,E4_low,E5_low,NA, E0_low),
           FCO2_low = c(F1_low, F2_low, F3_low, F4_low, F5_low, sum(F1_low, F2_low, F3_low, F4_low, F5_low), F0_low),
           kCO2_high = c(k1,k2,k3,k4,k5, NA,k0),
           E_high = c(E1,E2,E3,E4, E5,NA, E0),
           FCO2_high = c(F1, F2, F3, F4, F5, sum(F1, F2, F3, F4, F5),F0))


kable(bin_FCO2, digits = 2, col.names = c("A = lake area in km2","mean pCO2, uatm","mean kCO2, m2/d","mean ECO2, g/m2/y", "binned FCO2, MtCO2/y","kCO2, m2/d","mean ECO2, g/m2/y", "binned FCO2, MtCO2/y"), caption = "Finland") %>% kable_styling() %>% 
  add_header_above(c("Lake class" = 1, " " = 1, "Low estimate" = 3, "High estimate" = 3)) %>%
  group_rows(group_label = "All lakes", start_row = 7, end_row = 7)

Table 6.4: Finland

Lake class		Low estimate			High estimate
A = lake area in km2	mean pCO2, uatm	mean kCO2, m2/d	mean ECO2, g/m2/y	binned FCO2, MtCO2/y	kCO2, m2/d	mean ECO2, g/m2/y	binned FCO2, MtCO2/y
A < 0.1	1271.00	0.72	185.29	0.17	0.95	240.97	0.22
0.1 < A < 1	1164.08	0.73	157.86	0.72	1.10	240.48	1.10
1 < A < 10	1075.72	0.78	146.08	4.34	1.41	264.03	7.85
> 10	1081.07	0.78	138.73	12.65	1.66	299.92	27.36
Big lakes (> 100)	966.56	0.81	122.24	6.61	2.03	306.00	16.53
Total				24.49			53.06
All lakes
All lakes	1162.98	0.75	161.04	20.36	1.20	253.15	32.00

6.7 Compare with Raymond et al. (2013)

Raymond et al. (2013) estimate the CO2 emissions as gC/m2 land/year. We convert our estimated median CO2 evasion rate from gC/m2/year to gC/m2 land/year by multiplying it by the water area in a given region, and then dividing it by the land area.

inland.waters.nor <- 20221 * 1e6 # km2 to m2, @SSB
land.nor <- land <- 323806 * 1e6 # km2 to m2, @SSB
inland.waters.swe <- 4014169.92 * 1e4 # ha to m2, @SCB
land.swe <- 444435 * 1e6 # km2 to m2
inland.waters.fin <- 34515 * 1e6 # km2 to m2, @Statfi
land.fin <- 338478 * 1e6 # km2 to m2

tot.water <- inland.waters.nor + inland.waters.swe + inland.waters.fin
tot.land <- land.nor + land.swe + land.fin

mean.eco2.high <- c(median(nlss$ECO2_toc, na.rm = T)*365, #NLSS # in gC/m2/year
                    with(subset(nlss, nation == "Norway"), median(ECO2_toc, na.rm = T)*365),
                    with(subset(nlss, nation == "Sweden"), median(ECO2_toc, na.rm = T)*365),
                    with(subset(nlss, nation == "Finland"), median(ECO2_toc, na.rm = T)*365))

mean.eco2.low <- c(median(nlss$ECO2_toc_low, na.rm = T)*365, #NLSS # in gC/m2/year
                    with(subset(nlss, nation == "Norway"), median(ECO2_toc_low, na.rm = T)*365),
                    with(subset(nlss, nation == "Sweden"), median(ECO2_toc_low, na.rm = T)*365),
                    with(subset(nlss, nation == "Finland"), median(ECO2_toc_low, na.rm = T)*365))                    
                    
land.eco2.high <- c(mean.eco2.high[1]*tot.water/tot.land,
                    mean.eco2.high[2]*inland.waters.nor/land.nor,
                    mean.eco2.high[3]*inland.waters.swe/land.swe,
                    mean.eco2.high[4]*inland.waters.fin/land.fin)

land.eco2.low <- c(mean.eco2.low[1]*tot.water/tot.land,
                    mean.eco2.low[2]*inland.waters.nor/land.nor,
                    mean.eco2.low[3]*inland.waters.swe/land.swe,
                    mean.eco2.low[4]*inland.waters.fin/land.fin)
                    

kable(tibble("Country" = c("All 3", "Norway", "Sweden", "Finland"),
            "Water"= c(tot.water, inland.waters.nor, inland.waters.swe, inland.waters.fin),
            "Land" = c(tot.land, land.nor, land.swe, land.fin),
            mean.eco2.high,
            land.eco2.high,
            mean.eco2.low,
            land.eco2.low),
      col.names = c("Country","Water area, km2", "Land area, km2", "Median ECO2, gC/m2/year", "Median ECO2, gC/m2 land/year", "Median ECO2, gC/m2/year", "Median ECO2, gC/m2 land/year"),
      digits = 2) %>% kable_styling() %>%
  add_header_above(c(" ","Area" = 2, "High estimate" = 2, "Low estimate" = 2))

	Area		High estimate		Low estimate
Country	Water area, km2	Land area, km2	Median ECO2, gC/m2/year	Median ECO2, gC/m2 land/year	Median ECO2, gC/m2/year	Median ECO2, gC/m2 land/year
All 3	94877699200	1.106719e+12	176.27	15.11	107.48	9.21
Norway	20221000000	3.238060e+11	41.36	2.58	24.20	1.51
Sweden	40141699200	4.444350e+11	210.77	19.04	132.31	11.95
Finland	34515000000	3.384780e+11	236.71	24.14	143.70	14.65

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